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Agent-Based Computational Modeling and International Relations Theory: Quo Vadis?

Summary and Keywords

Agent-based computational modeling (ABM, for short) is a formal and supplementary methodological approach used in international relations (IR) theory and research, based on the general ABM paradigm and computational methodology as applied to IR phenomena. ABM of such phenomena varies according to three fundamental dimensions: scale of organization—spanning foreign policy, international relations, regional systems, and global politics—as well as by geospatial and temporal scales. ABM is part of the broader complexity science paradigm, although ABMs can also be applied without complexity concepts. There have been scores of peer-reviewed publications using ABM to develop IR theory in recent years, based on earlier pioneering work in computational IR that originated in the 1960s that was pre-agent based. Main areas of theory and research using ABM in IR theory include dynamics of polity formation (politogenesis), foreign policy decision making, conflict dynamics, transnational terrorism, and environment impacts such as climate change. Enduring challenges for ABM in IR theory include learning the applicable ABM methodology itself, publishing sufficiently complete models, accumulation of knowledge, evolving new standards and methodology, and the special demands of interdisciplinary research, among others. Besides further development of main themes identified thus far, future research directions include ABM applied to IR in political interaction domains of space and cyber; new integrated models of IR dynamics across domains of land, sea, air, space, and cyber; and world order and long-range models.

Keywords: international relations, IR theory, agent-based modeling ABM, computational modeling, social science methodology, formal models in social science, computer models, object-oriented modeling, empirical international relations theory

Introduction

What Is an ABM?

An agent-based computational model in international relations (IR) is an object-oriented simulation model of a system of political entities that interact on foreign policy issues on an organizational scale or “level of analysis” (country, relational, regional, or global). Accordingly, the landscape of theory and research on agent-based computational IR varies in terms of such components (specific systems, issues, and scales) and their combinations across different ABMs. In order to assess and understand ABMs in IR it is worthwhile to take a closer look at each dimension and its combinations, which defines the structure and state of the field.

Two preliminary terminological clarifications are in order. First, the acronym “ABM” is used to denote (1) an agent-based computational model, as well as (2) agent-based modeling as a specific methodology that is used in many domains of science (social, natural, and engineering), with meaning usually clarified by context. Second, the term “computational” is always implied in reference to ABM, because there are many agent-based models that are not necessarily computational, such as game-theoretic models, Richardsonian conflict models, and others where actors are the fundamental units of analysis.

The methodology of ABM in IR theory and research is summarized in Figure 1. The process begins by selecting a part of the IR real-world universe to study (explanandum, in the lower center). In a way that parallels other formal approaches (e.g., mathematical modeling), an abstraction selects a set of concepts, entities, research questions, and other modeling elements to create a formal model. In this case the formalization uses a computational structure, such as provided by a preexisting toolkit (e.g., MASON, NetLogo, Repast, or other) or by native code in some object-oriented programming (OOP) language (see Section “Object Oriented Modeling (OOM) and Object Oriented Programming (OOP),” below). Once the agent-based simulation model is created (explanans, in the upper right side of the cycle), it must then be subject to verification and validation tests with empirical data. A sufficiently verified and validated model is considered ready for analysis of scenarios, “what if” research questions, and other scientific uses.

Agent-Based Computational Modeling and International Relations Theory: Quo Vadis?Click to view larger

Figure 1. Formal methodology of agent-based modeling applied to international relations theory.

Note: Adapted from Cioffi-Revilla (2017, ch. 8).

Complexity of IR and ABMs

First, international relations phenomena are complex, in a strict scientific sense, because they generally satisfy the characteristics of complex phenomena (Byrne & Callaghan, 2014; Cioffi-Revilla, 2017, ch. 1, 7; Conte et al., 2012; Epstein, 1999; Page, 2015; Paravantis, 2016):

  1. 1. Cardinality. The number of agents or entities in the international system, as well as in IR ABMs is large. For example, in every epoch the international system is composed of multiple actors, even during bipolar epochs.

  2. 2. Diversity. In addition to being large, entities are diverse in nature, including state and non-state actors, relations, and dynamics.

  3. 3. Dimensionality. The state of each entity in an international system is determined by many variables and parameters, so IR phenomena and their ABMs have what is known in systems terminology as “high dimensionality.” Note that dimensionality, cardinality, and diversity represent separate aspects of a complex system, not the same dimension of complexity. Examples include goals, capabilities, vulnerabilities, allies, dependencies, and infrastructure, and relevant geospatial features, among others.

  4. 4. Connectivity. Entities and dynamics in IR phenomena and in ABMs are linked or interact through interaction network structures that connect agents and entities. Organizations, both internal and external (e.g., alliances) to each actor, provide typical examples of connectivity structures.

  5. 5. Nonlinearity. Patterns of interactions in IR and in ABMs are generally nonlinear, as opposed to linear dependencies in simple systems. This property is primarily responsible for generating emergent phenomena at macro-levels above the individual entities, such as emergent relational, regional, systemic, or global phenomena (polarization, warfare, alliances, international regimes and organizations). For example, perceived security threats are a nonlinear function of objective threat conditions (a phenomenon known in psychology as the Weber-Fechner law); and compound events in deterrence are exponentially related to the number of deterrence requirements (Wohlstetter, 1959, 1968); among other known patterns, so foreign decisions are the result of anything but linear thinking or simple processes (see, e.g., Cioffi, 1989, 2017, ch. 6; Zinnes & Gillespie, 1976; Zinnes & Muncaster, 1987; Zinnes et al., 1978).

Multiple Modeling Scales

The scale of IR ABMs is at least three-dimensional, according to organization, space, and time.

  1. 1. Organizational scale. An IR ABM may range from single-actor decision making, to group decision making (e.g., bureaucratic systems or processes), or be national, regional, or global in organizational scope.

  2. 2. Spatial scale. The geographic scope of an ABM, when specified, determines its spatial scale. While some models include two countries, others include several or the entire international system.

  3. 3. Temporal scale. IR ABMs operate on a time-scale of that range from tens of milliseconds (human decision making) to millennia (rise and fall of civilizations). ABMs of the international system of states are typically calibrated on a scale of years and run through several centuries.

Methodologically, therefore, every IR ABM can be situated in a three-dimensional space consisting of the above dimensions. From simplest to most complex, in relative terms, IR ABMs range from the most individualistic (e.g., a single agent decisionmaker), referencing a single actor (e.g., within a foreign policy bureaucracy or agency), with a short temporal range (e.g., a single decision in time); to the most comprehensive political collective (global system), in all continents and space where political agents interact (governmental and non-governmental), from the origin of politics in complex societies to the present (the so-called long-range consisting of the past 10,000 years). The organizational (O), geospatial (G), and temporal (T) scales of a political ABM specify its “OGT scale,” which is more accurate than simply referring to a two-dimensional spatio-temporal scale. The OGT scales generate a three-dimesnional space where each model is situated and may be compared to others.

Object-Oriented Modeling (OOM) and Programming (OOP)

While IR ABMs differ in terms of complexity, OGT scales, and other specific characteristics, they all have the object-oriented modeling (OOM) paradigm of computational social science in common. The defining feature of OOM is the focus on political entities, which comprise (“encapsulate” in proper OOM terminology) variables and dynamics. By contrast, other modeling methodologies, such as statistics and equation-based mathematical models in social science focus primarily on variables, leaving actors implicit. Two examples of OOM theory in IR are deterrence theory and balance of power theory, because the units of analysis in each case consist of countries (strategic actors) which, in turn, consist of capabilities and other features. In other words, strategic capabilities are conceptualized as constituent attributes of actors, not as separate or isolated variables. By contrast, a Richardsonian arms race model is more directly focused on variables such as levels of armaments or hostility, rather than being primarily focused on the actors themselves.

A significant methodological implication and theoretical advantage of the object orientation of ABM is that it enables the researcher to include essential but often heterogeneous features of IR within a single integrated model, such as the environment of the international system being modeled, capabilities, belief systems, norms, energy and information flows, hierarchies and networks of couplings and embeddedness, systems-of-systems, and similar real-world features and phenomena. Modeling such features is often impossible or intractable through other approaches, such as statistical or traditional mathematical models.

Computational IR

The ABM approach to IR theory is a specific modeling methodology and scientific tradition within the broader field of computational social science, which comprises several other modeling traditions, such as complexity theory, network science, microsimulation, and system dynamics, among others (see Cioffi-Revilla, 2017; Gilbert & Troitzsch, 2005; Taber & Timpone, 1996). Hybrid ABMs are those that combine agent-based computational components with other nonagent formal structures, such as system dynamics (e.g., Boyle et al., 2006) or evolutionary learning (Cioffi, De Jong, & Bassett, 2012). Hybrid ABMs have grown in quantity and quality as researchers have gained familiarity with computational modeling methods to fulfill theoretical needs.

Why ABMs Support Interdisciplinary Research Necessary for Understanding Politics

Finally, as a field of computational social science, ABM research in fields such as IR is subject to the same opportunities, limitations, and other operating aspects as agent-based modeling research in other fields in the natural, social, and engineering sciences where computational simulation modeling is used. A major property of ABM is its powerful capacity for interdisciplinary integration across subject matter necessary for IR theory. For example, ABM can integrate political with social, cultural, economic, geographic and other aspects necessary to create viable regional or global models of the international system (Cioffi, 2016). This is also the reason why much research on social ABMs is presented at conferences in many fields, including natural science and engineering sciences conferences, not just in social science. Purely mathematical, noncomputational models are more limited in this regard, given the complexity of interdisciplinary models (Bonabeau, 2002).

Chronological Overview of ABM in IR

This article focuses on peer-reviewed IR ABM research published in recent years, as well as on earlier models that somehow have escaped the attention of other reviewers but hold high significance. Peer-reviewed publications include traditional journals and academic presses, as well as PhD dissertations, refereed conference papers, and post-conference proceedings, among others. The total population of such channels has grown significantly over time, as progress and interest in the field has grown.

Table 1 contains the results of surveying the large field of ABMs in IR using the three dimensions of IR in terms of organizational, geospatial, and temporal scales. Column 1 provides a name and number that identifies each ABM. Some modelers name their models (e.g., GeoSim, MayaSim, AfriLand), while others do not, so a name is assigned to models that appear to lack a name. The practice of naming models is to be encouraged, for it facilitates referencing and omits having to always name the authors or make an arbitrary selection of authors. Column 2 provides a brief description of the referent system in the empirical world (i.e., the system being modeled) and the phenomenon or theme being investigated within the system. Column 3 specifies the approximate degree of empirical fidelity of the ABM, with low meaning highly abstract or theoretical, high meaning that a large amount and variety of empirical data or validated mechanisms were used to build the model, and medium being somewhere in between. Clearly, values of empirical calibration or fidelity are somewhat subjective and intended only as coarse measures so as to categorize ABMs on a simple scale of abstraction. Column 4 specifies the programing language or toolkit used to implement the model in code. Finally, Column 5 provides references to one or more publications where the model is documented. Each model is listed in chronological order of the year in which it was first published.

Table 1. Agent-Based Computational Models in International Relations by Date of Publication

Model number and name

Referent system; research themes

Abstract scale

Source code

Publications

1977

1. Machiavelli in Machina

International state system; conflict

Medium

FORTRAN

Bremer & Mihalka, 1977

1980

2.Computational 2-Person Iterated Prisoner’s Dilemma

Multi-actor system; emergence of cooperation

Low

Axelrod, 1980a, 1980b, 1981, 1984, 1986, 1987; Axelrod & Dion, 1988; Wu & Axelrod, 1995

1986

3. Norms Game

Multi-actor system; norm emergence and stability

Low

Axelrod, 1986, 1987

1990

4. Realpolitik Among Hexagons

International state system

Medium

Cusack & Stoll, 1990

1992

5. Concurrent Interstate Conflict

International system; onset of wars, alliances

Medium

Lisp

Duffy, 1992, 1993

1993

6. Landscape Theory

International state system; alliance formation

Medium

Pascal

Axelrod & Bennett, 1993; Axelrod, 1997 in R; Bennett, 2000 in Pascal

1994

7. EOS

Neolithic polities system

Low

Doran et al., 1994

1995

8. Tribute Model

International state system

Low

Pascal

Axelrod, 1995

1997

9. ISAAC

Landscape of combat; emergent phenomena of military combat

Medium

ANSI C and EINSTein (C++)

Ilachinski, 1997, 2004, 2005, 2012

10. GeoSim

Balance of power system; territorial change

Medium

Repast

Cederman, 1997, 2001, 2002, 2003; Cederman et al., 2010, 2011; Cioffi & Gotts, 2003; Johnson et al., 2011

2000

11. Two-Level National Security Management

International state system with domestic opposition actors; maintaining security and democracy

Medium

Pascal

Simon & Starr, 2000

2002

12. Economic Geography, Trade and War

International state system; onset of war

Medium

Gauss

Bearce & Fisher, 2002

13. Civil Violence

Generic agent society; onset of civil violence warfare

Low

Sugarscape

Epstein, 2002

14. War and Trade

International state system; emergence of war

Medium

C++

Min, 2002; Min et al., 2004

15. Client States

International system; formation of U.S. client states

Medium

Repast

Sylvan & Majeski, 2002, 2003

2003

16. Radical Islamist Terrorism TAP

Middle East and North Africa (MENA) region; onset of terrorism

High

Java

MacKerrow, 2003

17. Historical Dynamics

System of polities; rise and fall of polities

Low

APL

Turchin, 2003

2004

18. Etruscan Politogenesis

Regional Etruscan polity system; emergence of politogenesis

High

NetLogo?

Cecconi et al., 2004, 2015

19. Emergent Polarity

International system; emergence of polarity

Low

Pascal

Cederman, 2004

20. Asymmetric Power

International system with asymmetric power; emergence of cooperation

Low

C+

Majeski, 2004, 2005

21. Silk Road Simulation

Network of silk road polities; emergence and self-organization

Medium

Java

Malkov, 2004, 2006

22. Conflict Wargame

International system; strategic-operational effects of conflict

High

Aide de Camp 2 (AIDE2)

Selke, 2004

2005

23. Bronze Age Mesopotamia

Mesopotamian polities system; emergence of sociopolitical complexity

High

ENKIMDU

Christiansen & Altaweel, 2005, 2006; Wilkinson et al., 2007

24. International Norms

International system; emergence of international norms

Medium

Hoffmann, 2005, 2006, 2008

25. TNet-CTNet

Complex adaptive system of terrorist and CT networks; emergent evolving networks

Medium-High

SOTCAC in C++

Ilachinski, 2005, 2012

2007

26. Small-Scale Chiefdoms

Small-scale agent society; politogenesis

Medium

C++

Alden & Choi, 2007

27. Titicaca Warfare

Titicaca regional polities system; conflict

Medium

NetLogo

Griffin & Stanish, 2007; Stanish & Levine, 2011

2008

28. REsCAPE

Society with ethnic groups; onset of conflict and warfare

Framework

Java

Bhavnani, 2008; Bhavnani & Miodownik, 2009

29. Hierarchies

Inner Asia regional system; conflict among polities

High

MASON

Cioffi et al., 2011; Cioffi, Honeychurch, & Rogers, 2015; Rogers, 2017

2009

30. AfriLand

Regional international system; political stability, transnational conflict

Medium

MASON

Cioffi & Rouleau, 2009a, 2009b

2010

31. Cycling Polities

System of chiefdoms; cycling over time

Medium

Matlab

Gavrilets et al., 2010; Turchin et al., 2013

2011

32. Peruvian Politogenesis

Aspero polity and Norte Chico region, Supe River Valley, Peru; polity formation

High

NetLogo

Auble, 2010; Auble & Cioffi, 2013; Cioffi-Revilla, 2017, pp. 335–341

33. SOC and Polity Cycling

Population landscape; emergence of polities

Medium

NetLogo

Griffin, 2011

34. NormSim

International system; emergence of international norms and institutions

Medium

MASON

Rouleau, 2011

2012

35. RiftLand

East African regional international system; disasters, crises, conflict

High

MASON and GeoMASON

Cioffi et al., 2012; Kennedy et al., 2010, 2012; Sutherland, 2012

36. SW Puebloan

Puebloan polities system; collective goods

High

Kohler et al., 2012a, 2012b

37. Identity Conflicts

Interstate system with identities; emergence of conflict

Medium

NetLogo

Gartzke & Weisiger, 2013

2013

38. Canonical Polity Cycling

Politogenesis; emergence and cycling of first complex polities

Medium

NetLogo

Dover, 2013; Dover & Cioffi, 2015

39. MayaSim

Maya polities system; polity dynamics

High

NetLogo

Heckbert, 2013

40. Spatial Tribute Model

International state system

Low

MASON

Masad, 2013

41. Baghdad Sunni-Shiite War

Baghdad, Iraq; warfare between Sunnis and Shiites

High

Weidmann & Salehyan, 2013

2014

42. Jerusalem Segregation and Violence

Jerusalem, Israel; segregation and emergence of urban violence

High

Repast and Java

Bhavnani et al., 2014

2015

43. Northern Jazirah Politogenesis

Regional Northern Jazirah polities system, Iraq; emergence of polity settlement hierarchies

High

Repast

Altaweel, 2015

44. NorthLands

Boreal and Arctic regions; climate change and sociopolitical adaptation

High

MASON and GeoMASON

Cioffi et al., 2015, 2016

45. Paths to Great Power War

International multipolar state system; onset of great power war

Medium

NetLogo

Luteijn, 2015

2016

46.ZambeziLand

Zambezi River, Southern Africa; polity formation

Medium

Python

Bogle & Cioffi, 2016

47. CLM-2016

Pacific region international system; deterrence, proliferation nukes

High

Construct

Carley et al., 2016

48. Masad, 2016

International system; conflicts and crises

Medium

Python

Masad, 2016

49. Maidan

Contemporary Ukrainian society; collective action vs. Russian annexation

Low

NetLogo

Pugacheva, 2016, pp. 354–365

50. Referenda v. Propaganda

Global system; top-down and bottom-up institutional effects

Low

Java

Ulloa et al., 2016

2017

51. RealLand

International state system; onset of war, alliances, territorial dynamics

High

NetLogo

Selke, 2017; Cioffi-Revilla, 2017

Note: Self-organized terrorist-counterterrorist adaptive coevolution.

Source: Prepared by the author.

The reader will note that numerous international conflict models are included in this survey of ABM in IR theory and research. However, not all forms of conflict or warfare are included, given the international orientation of this survey. For example, ABMs of purely internal or civil violence (e.g., Bahvnani & Choi, 2012; Bennett, 2008; Cioffi & Rouleau, 2010; Collins et al., 2013; Goh et al., 2006; Harrison, 2016; Keller et al., 2010; Kuznar, Sedlmeyer, & Kreft, 2008; Makowski & Rubin, 2013; McFarlane, 2016; Weidmann, 2016) are omitted, as they more properly belong to the broader realm of politics or political science, such as comparative politics, political sociology, or political anthropology. On the other hand, ABMs of transnational conflict that spills over more than a single country or polity are included (e.g., Axelrod, 1997; Bhavnani et al., 2014; Ilachinski, 2012; MacKerrow, 2003, Pugacheva, 2016; Ulloa et al., 2016).

ABMs of polity formation (e.g., Axelrod, 1995; Bogle & Cioffi, 2016; Cederman, 1997; Doran et al., 1994; Masad, 2013) are included within the scope of this survey, given the fundamental nature of polities as building blocks of international systems. Recall that polities vary according to organizational scale, so instances include chiefdoms, states, empires, and the global polity system in recent centuries.

Areas of Theory and Research

Table 1 would have been a lot smaller if the survey had been confined to models of the contemporary international system. However, such a restriction would have greatly diminished the value of ABM. Accordingly, this assessment includes ABMs of ancient and current international systems, small and large units, and brief and long epochs of time. ABM methodology is viable across the full range of all three “OGT” dimensions mentioned earlier: organizational, geospatial, and temporal.

Given the several dozen ABMs identified in Table 1, it seems useful to highlight several areas of IR theory and research that form clusters of scientific inquiry. The many ABMs that populate Table 1 represent a great variety of models contributed by computationally oriented political scientists, archaeologists, and computer scientists, to name some the main disciplines involved in this interdisciplinary effort.

IR ABMs identified in Table 1 also vary in terms of (1) system complexity, (2) substantive phenomena (e.g., norms, warfare, trade, alliances, and combinations thereof), and (3) OGT scales (organizational, geospatial, and temporal dimensions). At one end of the spectrum are simple models focused on a single theme involving one or few actors within a relatively short time span (e.g., models 3, 7, 8, 13, and 17). At the other end of the spectrum are models composed of numerous heterogeneous actors in dynamic interaction over many themes or issues during a long period of history (e.g., 16, 23, 29, 35, and 41).

The main themes investigated by the ABMs in Table 1 have been numerous, diverse, and include the following: polity formation, foreign policy decision making, conflict and polity dynamics, transnational terrorism, politics of international trade, international cooperation, alliances, norms, and effects of climate change. Each of these themes represents a cluster of research questions.

Polity formation at all levels or scales of organization is a clear theme that has emerged over the past decades. The phenomenon of polity formation is also known as politogenesis (Cioffi-Revilla, 2017, chs. 5, 7), a term originally introduced by Russian computational social scientists (Bondarenko & Korotayev, 2011; Grinin, 2009; Grinin & Korotayev, 2009). Polity formation refers to the first (i.e., earliest) emergence of chiefdoms, states, and empires in human societies in various parts of the ancient world, from a long-range historical perspective (Auble, 2010; Auble et al., 2013; Bogle & Cioffi, 2016; Cecconi et al., 2015; Cioffi-Revilla, 2017, chapter 5). Polity formation also refers to the formation of a generic polity or political system, in terms of norms, hierarchies, or control mechanisms, regardless of time or space, from a more abstract or theoretical perspective (Alden & Choi, 2007; Axelrod, 1995; Cederman, 1997; Dover, 2013; Dover & Cioffi, 2015; Gavrilets, Anderson, & Turchin, 2010). In addition, besides instances consisting of state and nonstate polities, polities can also form in network-oriented or transnational forms, as in the case of terrorist organizations with putative or ideologically claimed control or governance over a set of individuals or community. ABMs of polity formation are and will remain essential in IR theory and research, because polities of all types or organizational forms are fundamental to international relations (Cioffi-Revilla, 2017, chs. 5–7).

Foreign policy decision making has been another IR ABM cluster, based on earlier work centered on developing a deeper understanding of how leaders and foreign policy elites make decisions in the international system (Simon & Starr, 2000; Sylvan & Majeski, 2002, 2003; Taber & Timpone, 1996). ABMs provide an ideal modeling framework for implementing theories of decision making, given their ability to render an ecology of relevant actors connected through various information and influence and control channels. Although some foreign policy ABMs have been informed by specific historical actors and circumstances, others are more theoretical or abstract, as was the case in earlier categories and in several of those identified below. A specifically valuable feature of ABMs in this area is their ability to implement algorithms that accurately reflect known practices and procedures in foreign policy and national security bureaucracies, in both formal and informal channels. Hence, this is an area where the information-processing paradigm of computational social science plays a central role.

Conflict, warfare, and polity dynamics has been a major focus of IR ABM theory and research. Although the majority of models in this area references modern or contemporary international systems (e.g., Alt et al., 2009; Bahvnani et al., 2014; Bennett, 2008; Cederman, 2003, 2008), several models already exist of earlier, formative epochs (Doran & Palmer, 1995). Most models in this cluster consist of statelike agents in interaction with one another. The environment in which they interact varies widely across models, ranging from highly abstract tilelike topologies to high-resolution landscapes consisting of terrain, hydrology, climate, and infrastructure (e.g., Kennedy et al., 2012). Regardless of their level of realism or data-intensive detail, all models in this category thus far consist mainly of land and limited air space. This category of models represents the closest we have so far in terms of a computational science of IR history, including its origins thousands of years ago (Cioffi-Revilla, 2017, ch. 5). As mentioned in section “Directions for the Future,” the ABMs in this survey do not include the full environment of the contemporary international system, including land, sea, air, space, and cyber (LSASC) domains. Although most of the ABMs in this cluster have been state-based, some have been network-oriented and have used clever diffusion mechanisms to represent dynamics (Malkov, 2004, 2006).

Transnational terrorism constitutes another cluster of IR ABMs (e.g., Bhavnani et al., 2014; Ilachinski, 2005, 2012; MacKerrow, 2003). (Note that this category in Table 1 excludes models involving strictly domestic terrorism, which is not an IR area of research.) ABMs in this cluster represent a smaller number than those ABMs that have focused on domestic violence and single-country terrorism. There is some underrepresentation in this category, however, because some of the ABMs that have been created in this area have remained unpublished (in the so-called gray literature) or are actually classified as secret by government agencies, for understandable reasons. There is still an abundance of well-published models in this cluster, which is enough to represent a vibrant and active research area. This is an area where comparative computational analysis (so-called model-to-model or M2M comparative research) could be fruitful, particularly when using aspects of complexity in terrorism: cardinality, dimensionality, and other components discussed earlier in Section “Introduction”.

Cooperation was among the first clusters to form, based on computational modeling of IPD (Iterated Prisoners’ Dilemma) games (Axelrod, 1984). This research program inspired a generation of researchers in computational social science, well beyond IR theory. In IR itself, ABMs of international cooperation have also inspired numerous new insights into processes ranging from arms control to trade, the latter constituting an area that could be considered its own cluster (Min, 2002; Min et al., 2004), as well as norms (Axelrod, 1986; Bhavnani, 2006; Hoffmann, 2005; Rouleau, 2011) and alliances (Axelrod & Bennett, 1993; Bennett, 2000; Gartzke & Weisiger, 2013). Indeed, cooperation represents a superclass of IR ABMs, much like conflict, so separate clusters on aspects of cooperation are clearly discernable in Table 1.

Climate change has generated a cluster of IR ABMs in the early 21st century (e.g., Cioffi et al., 2015), thanks to several key developments. Besides the necessary interdisciplinary cooperation to undertake this category of computational models (and multiyear funding), Simons’s theoretical triad of human, artificial, and natural (HAN) systems (specifically, the coupled, adaptive, evolving dynamics; Simon, 1996), and the increasing availability of remote sensing data as well as detailed climate data with sufficient resolution, has enabled a new class of ABMs that would have been unthinkable just a few years earlier. In addition, powerful platforms or toolkits, such as MASON and Repast, have made possible scientific work of a kind that was simply not feasible before such systems existed. The idea that climate change can affect IR phenomena predates ABMs in this area, but it was not until the first computational simulation models were created that such effects could be demonstrated using coupled human-artificial-natural systems in specific geographic regions of the world (e.g., Cioffi et al., 2015). Such recent models will likely grow and improve to include phenomena linked to climate change, such as human migrations, infrastructure risks, and sociopolitical change.

Enduring Challenges

Most of the previous advances were achieved in spite of numerous, enduring challenges. The following are some of the major ones. Some can be remedied or mitigated; others are harder to overcome or need to be factored in, or managed as best as possible when conducting ABM research in IR. Additional challenges will no doubt arise when pursuing future research directions in Section “Directions for the Future”. Learning, publication, duplication, and achieving measurable accumulation of scientific knowledge will continue to pose enduring challenges.

Learning ABM in IR

Computational modeling is not part of the standard training of IR researchers, nor is mathematical modeling for that matter. Neither form of formal model (mathematical or computational) is part of the graduate curriculum. Exposure to ABMs in IR (or other areas of social science) at the undergraduate level is rare. Unlike students in other areas of science, exposed to mathematical and computational methods of scientific inquiry since high school, few social scientists experience similar exposure. Today, basic training in multivariate statistical analysis remains the core methodological toolset, just as it was twenty years ago.

The advent of effective and free teaching tools, such as NetLogo, is changing the educational landscape in ways that favor much earlier exposure to scientific ideas in IR. Many NetLogo models can be built and used by secondary or high school students to learn about social science, including history. This includes interdisciplinary fields such as IR, even if computational social science is not (yet) taught at pre-university levels. In addition, entertainment computational simulation games, such as Civilization and World of Warcraft (Bainbridge, 2010; van Creveld, 2013, ch. 6), among others, increase exposure to computational simulation modeling of international relations.

In the 1960s the teaching of physical and biological sciences in the United States was in disarray, leaving much to be desired—especially in light of Sputnik and other scientific accomplishments by Soviet scientists. As a response, the U.S. National Science Foundation instituted the Physical Sciences Study Committee and its biological counterpart. These efforts created new, excellent teaching materials, including innovative textbooks (PSSC, 1960) that instructed a new generation of physical and biological scientists. Perhaps comparable efforts are necessary today to advance computational social science and ABM approaches across the full spectrum of the social sciences, including IR.

Publishing an ABM

Political ABMs are difficult to describe in short publications (i.e., papers, chapters), and sometimes even in books. The main exceptions are doctoral dissertations (and master’s theses), which require extensive description and documentation of methods and modeling details. The need to use online “Supplemental Information” mitigates but does not entirely eliminate this challenge. Use of online depositories is valuable but does not solve all problems. Published code may still be difficult or impossible to comprehend, and therefore useless, unless it is written according to high standards. And the long-term sustainability of digital archives poses its own challenges.

The fundamental reason why ABMs are challenging to describe (with sufficient information so as to enable reproducibility) is that the referent system, as well as the simulation system, is complex, in the strict sense explained in Section “Introduction”: most IR ABMs are composed of numerous, diverse, and interconnected entities whose state is determined by many variables and parameters linked via nonlinear dependencies. Processes of adaptation and evolution make description additionally demanding. Mathematical, graphical, algorithmic, and other types of descriptions are all necessary, not optional. By contrast, most statistical models are relatively easier to describe, even when they have nonlinear, time-dependent, or probabilistic components. Complexity in ABMs also raises the issue of Occam’s Razor: the enduring balance between abstract simplicity and realistic representation (Edmonds & Moss, 2005).

Existing protocols for describing ABMs in general, or for use in other fields (e.g., the ODD protocol used in “individual-based” models in ecology; Railsback & Grimm, 2012; Object Design and Description), are only somewhat useful for social and IR ABMs. This is because extant protocols such as ODD were created for biological entities in mind, not for modeling entities such as people, belief systems, decision making, human groups, norms, networks, and political institutions. Accordingly, ABM description protocols created in other disciplines have an inherent tendency to fall short of what is needed to describe IR ABMs with sufficient information to enable reproducibility.

We need new protocols, perhaps through extensions of extant frameworks, such as the now popular ODD, augmented by proper human and social components, as well as specific details on complexity features. For instance, additional information on agent decision-making features, networks structures, evolutionary characteristics, among others commonly found in IR ABMs, would improve IR ABM descriptions. Another strategy for improvement could be the use of formal systems protocols, such as SysML (Systems Modeling Language; Delligatti, 2014; Friedenthal et al., 2015). Even without these more specialized systems protocols, more extensive use of UML (Unified Modeling Language) class, sequence, and state diagrams would go a long way toward improving the current situation (Cioffi-Revilla, 2017, pp. 53–73).

Avoiding Reinventing the Wheel

Although the number of existing IR ABMs may seem relatively large at fifty or so, a surprisingly small number of them appear to be based on a thorough assessment of prior work. This challenge seems sufficiently present (and corrosive of scientific practice) to warrant highlighting. In fact, some publications after the year 2000 lack references to prior literature, as if IR ABM were being invented ex nihilo. Few publications seem founded on thorough familiarity and understanding of prior models focused on the same or similar phenomena and can claim to advance knowledge through a systematic strategy of model development that builds on earlier research done by others.

Ideally, an ABM should be grounded and build on prior models in the same or neighboring themes, unless a demonstrably superior fresh start is being proposed on the basis of a thorough and well-documented assessment of prior work. The risk is otherwise high of reinventing the wheel, and not even realizing that similar or even scientifically superior wheels have already been created.

Accumulation of Knowledge

A related (and arguably greater) risk in the use of ABM in IR, when models are poorly or loosely grounded in earlier work, consists of failing to accumulate knowledge. All too often an ABM model fails to reflect greater scientific information and understanding of real world dynamics than its predecessors. This occurs for a variety of reasons beyond failure to check prior literature. For example, a modeler selects a language that is incapable of implementing desirable features found in earlier models, representing “a step backward,” or a more limited single-processor version is implemented and claimed as novel when earlier distributed versions accomplished more.

Ideally, every ABM on a given theme or cluster of research questions should provide a net advance in terms of scientific knowledge. This should be demonstrated explicitly, not simply assumed or alluded to in implicit arguments. As is the case with mathematical models, the power of computational models (agent-based or otherwise) lies in their ability to build on previous models and advance the frontiers of knowledge, such that each generation of IR scientists literally knows more about international relations phenomena than any previous generation.

Evolving Standards and Methodology

As in all fields of contemporary science, computational theory and methodology in IR is a work-in-progress: an evolving enterprise involving a community of practitioners. A major challenge involves keeping up with the latest ideas in areas of computational concepts, theories, models, programming languages, data structures, algorithms, and technologies that support their implementation. This is particularly challenging, because relevant developments originate from within the IR research community itself, as well as from the broader computational sciences community.

For example, several years ago the introduction of GPUs (graphics processing units) seemed to provide a revolutionary solution to overcoming problems of computational speed in large-scale multiagent systems. This idea seemed especially appealing for solving research problems in computational IR requiring large numbers of agents to be included in a given model. As a result, practitioners who were interested in these developments had to meet the challenges of learning the technology, new programming environment, and other aspects in order to exploit the technology. Another example is the case of quantum computing, now looming in the horizon of computational modeling. These technological examples are typical of computational science, which is more independent on technical advances than mathematical modeling is as a less dynamic tool set or methodology.

Journals and reviewers in general bear special responsibility for being familiar with high standards and implementing them. This will remain a demanding challenge for the foreseeable future. Unlike mathematical models, where standards have existed for several centuries and the formal structures evolve more slowly, ABMs in computational science are younger and more rapidly evolving.

Interdisciplinary Research

The interdisciplinary nature of agent-based computational modeling poses advantages and disadvantages. Much of the content of this entry is based on the positive advantages provided by these new approaches. However, the disadvantages or risks of interdisciplinary research cannot be ignored, because this research creates many challenges as well as opportunities. First, interdisciplinary work requires paying attention to that undertaken in other disciplines. In turn, this necessitates gaining extensive, deep familiarity with the relevant literature, including journals, proceedings, and other sources of scientific information in other disciplines. Attending scientific meetings of disciplines far from one’s own original field is another requirement.

The challenges imposed by the rigors of interdisciplinary research go a long way in explaining why IR ABMs so often seem to lack sufficient grounding in relevant disciplines, or why communication across disciplines remains so challenging. Disciplines are also protectors of scientific “turf,” and incursions that are often perceived as uninformed or lacking in expertise are not only unwelcome—they are also rejected outright, as when significant contributions are ignored by discipline-based turf protectors. In IR ABMs this is a challenging problem that can be solved only by increasing and deepening education, scientific exchange, rigorous communication, and sustained collaboration across disciplines that for too long have been accustomed to “protecting their territorial integrity” often at the price of ignorance and lack of scientific progress. ABMs provide a scientific venue for overcoming such collective action problems.

Directions for the Future

This assessment of ABM in IR theory and research suggests a number of directions for future research. First, further development of all the main topics identified in Section “Areas of Theory and Research” is necessary and will likely continue, since ABM methodology and its broader complexity science has been far from being fully utilized. For example, few IR ABMs make extensive use of insights and understanding provided by complexity science, such as mathematical properties of results from simulations (e.g., Cederman, 2003; Cioffi, Honeychurch, & Rogers, 2015; Ilachinski, 2012). The amount of complexity science effective used by IR ABMs is still scant compared to its potential for scientific progress.

Second, from a purely methodological perspective, the research community will likely develop increasing interest in technological aspects of ABM approaches to IR theory and research. These would include the use of big data in phases of model development (from motivation to analysis), further use of GIS (geographic information systems) to support geospatial and environmental modeling when needed, new visualization facilities, advances in evolutionary computation, and parallel computing, among other possibilities. The latter has numerous aspects and architectures that are relevant to ABM in IR theory and research, such as for modeling cognitive structures that support richer representations of decision making, parallel distribution of interaction networks among agents, implications of Amdahls’ Law for gaining speed up with parallelized computations (Cioffi, 2014), and ways of overcoming challenges with model components that are computationally intensive, among others.

Third, from a more substantive perspective, a set of four additional themes readily suggests themselves, based on the assessment already provided in section “Areas of Theory and Research.”

Outer Space and Cyberspace

The contemporary international system is now as dependent on space-based (earth-orbiting technologies and similar systems) and cyber systems (the Internet and World Wide Web as information space) and processes as any other major aspect of civilization: that is, “space” and “cyber,” for short. Indeed, our society has become dependent on space and cyber for maintaining and enhancing our quality of life, as well as its fundamental viability. Accordingly, international relations today—from foreign policy decision making within the bureaucracies and executives of foreign ministries all the way to global strategic levels—critically depend on space and cyber systems. Leaders and publics from virtually all countries and regions of the world alike rely increasingly on cyber and space for a multitude of interactions and transactions on multiple scales, from local to global.

ABMs are fully capable of including space and cyber entities within their ontology. Such entities are human and technological, natural, and artificial, and consistent with concepts discussed earlier in Section “Introduction”. For example, consider the space domain. The satellite fleets of major powers in the contemporary international system—United States, EU, Russia, China, India, Brazil—as well as federated space-based assets, are a major component of national security capabilities. They are composed of people, organizational entities, norms, physical assets, and extensive and complex infrastructure systems. Both governmental and civilian entities are related through a network of dependencies.

In cyber, the ontology is not less complex, albeit quite different in terms of composition and topology. The World Wide Web, the physical Internet, and numerous critical cyber networks all provide essential information-processing and other forms of support to governmental and nongovernmental interactions in the international system. Governance of the Internet may not be governmentally controlled, but it still represents an issue of fundamental national security for all actors in the international system, especially the great powers. Cybersecurity dilemmas are no longer a matter of science fiction. The complexity of cybersecurity satisfies all essential features explained in Section “Introduction”: cardinality (large number of entities), dimensionality (many variables determine the state of entities), diversity (many different types of entities), connectivity (network structure of the cyberworld), and nonlinearity (emergent phenomena generated by interacting components).

Both space and cyber components of the international system are not only complex; they are also adaptive and evolutionary. This is mostly due to the advanced technological nature of cyber and space domains, as opposed to earlier and more traditional domains of the international system in terms of land (the oldest), sea, and air. Adaptation and evolution are distinctive features of advanced technologies, such as space systems and cyber systems. As complex adaptive system components of the international system, systems of space- and cyber-based components obey a variety of properties and governing principles, such as fitness functions of various kinds (e.g., single, multiple, and dynamic) that determine which systems are selected, maintained, and improved, and which are discarded from the technological landscape. For example, today leaders of most developed countries rely on technologically sophisticated systems of space-based communications supported by a constellation of satellite networks to exchange information on policy issues ranging from national security to economic development and global governance. All such systems are adapted and evolved from earlier generations of legacy systems. Whereas earlier land- and sea-based systems were subject to local weather, today’s space-based and cyber systems are vulnerable to space weather conditions that affect the integrity and viability of orbiting communications infrastructure. Such features and phenomena represent a challenge for improving ABMs in IR in areas such as information warfare, hybrid conflicts, and global public opinion dynamics, among others.

Integrated Models

Many IR ABMs today still lack proper integration. The current international system consists of land, sea, air, space, and cyber components. By contrast, most IR ABMs in Table 1 are limited to land alone, as if the world were still confined to conventional balance of power and ground-based interactions and strategies exclusively based on terrestrial combat. Clearly, a new generation of integrated ABMs is needed for representing the contemporary international system in modeling accurate ways to address research questions and phenomena resulting from the land-sea-air-space-cyber (LSASC) integration.

Besides integration of LSASC components and environments, integration also means composing IR ABMs in such a way that they include human, artificial, and natural (HAN) environments. This requires integration of all three components of the HAN triad (e.g., Cioffi, 2016; Kennedy et al., 2014), not just one or two at a time (e.g., Cederman & Girardin, 2007a, 2007b; Liu et al., 2007; Ostrom, 2009). No country exists independently of the land, sea, and air it is situated in, so IR theory and research stand to gain from inclusion of natural environments. HAN components are another way of viewing LSASC components and both serve the purpose of verifying completeness in IR ABMs.

From the substantive perspective of IR issues (transnational terrorism, national security, migrations, pandemics, alliances, foreign aid, arms control, nonproliferation), greater integration is also needed across issues, because polities in the international system concurrently deal with issues (i.e., in active parallel modes), not in sequential or serial processes (“one-at-a-time”). Concurrency in managing national security and policy issues on multiple spatial and temporal scales is a hallmark of governance in every polity. This is true at scales or levels from domestic, to national, to international, to global.

Properly designed ABMs are fully capable of handling the complexities of LSASC, HAN, and multi-issue integration. In addition, features of the international system include continuities and discontinuities, or continuous and discrete data, respectively. For example, both MASON and Repast have extensive discrete and continuous facilities for representing and processing information, including 3D, for data structures and complicated event scheduling, besides an increasing number of code libraries. The international system itself is a spherical topology of adjacent and remote actors, as an interaction network, not a flat 2D world as in a paper map, so different time zones and other real-world features affect daily interactions. While interactions today occur on a 24/7/365 basis, such a system requires both continuous and discrete data structures and algorithms for scientific modeling and simulation. Efforts in this direction will almost always require distributed architectures, which is an area where much exists already and can be leveraged. Also, the availability of such distributed systems will grow in the future.

World Order

The structure and dynamics of world order are fundamental and perennial themes in IR theory, but one that is only indirectly addressed by models in Table 1. This is arguably true on both regional and global scales, since world order is akin to a fractal or multiscale property: in politics, some system or pattern of structured order always exists at domestic, national, bilateral, multilateral, regional and global levels. The classical theory of world order, based on balance of power among the main actors or great powers, includes dynamic processes such as arms races and security alliances that explain war and peace.

In the early 21st century the only ABMs that are related to world order are mainly those that examine norms (e.g., Axelrod, 1986; Degterev, 2016 Hoffmann, 2008; Rouleau, 2011), not institutions such as specific historical alliances and forms of international governance. Although norms are significant for understanding world order, they are insufficient, especially in the computational reconstruction of major processes such as the system of Westphalian alliances, the Concert of Europe, the League of Nations, and the United Nations system of institutions. According to IR theory, each of these historical systems emerged from the ashes and failure analysis of the previous system in preventing general war. Reforming the current UN system or designing and implementing a new system of world order capable of preventing general war is a scientific and policy task that can be supported by appropriate agent-based modeling of international order to test and refine plans for improving international peace and security.

ABMs of world order need to explain how peace and war occur in the contemporary international system, specifically in terms of the polities and dynamics operating today, with proper nouns, not just in terms of nameless actors that rise and fall as in the Chinese game of Go. Real world countries require realistic, high-resolution detailed representations in terms of LSASC and HAN components, otherwise they are not sufficiently explanatory and, therefore, fail as empirical theories aiming to explain how the real-world works. Such high-fidelity ABMs must be virtual worlds in silico capable of replicating the known historical record and explaining the present and providing insight about future history of the international system.

Such ABMs of world order are feasible and desirable, given proper scientific planning and implementation. While the earliest proposals in this direction date to the early 2000s, as of this writing no one has yet created a high-fidelity ABM of the international system on a global scale—comparable, for example, to current weather and climate (long-range) models. However, there is sufficient progress with regional models to support a more global effort in this direction. A high-fidelity ABM of the entire international system today would require interdisciplinary organization, deep expertise in computational modeling, and rigorous reliance on best practices concerning the entire lifecycle of ABM based on the MDIVVA process summarized earlier in section “Introduction.”

Long-Range Models

No science is complete without explaining and understanding when, where, and how its phenomena began and how it evolved into its current form. All the IR ABMs discussed thus far may be designated as short-range in terms of temporal scale. Long-range IR theories are like theories in geology or cosmology: they explain the origin and total historical evolution of the international system, from the period of initial formation thousands of years ago to the present time. The international system has always been composed of state and non-state actors as the main two classes of entities. During its formative phase, the international system began with nonstate polities today called “chiefdoms” in social science. These early polity systems were frequently at war, and in some cases in constant warfare in the form of raiding and related violent interactions. Eventually some chiefdoms evolved into states, and later some states evolved into empires, forming the first inter-state international systems. Other forms on nonstate polities, such as terrorist actors and international organizations eventually appeared.

Long-range ABMs of IR are another future research direction. Above all, they should be capable of generating thousands of years of history, not just decades or centuries, because the long-range scale of the international system is empirically millenarian. Moreover, initial conditions for such long-range ABMs correspond to hunter-gatherer societies, because they generated the first chiefdom-level polities that constituted the earlier interpolity system. The formation of chiefdom-based interpolity systems occurred independently at least four times in different and far flung regions of the ancient world: the Near East or West Asia, ca. 10,000 years ago; the Far East or East Asia, ca. 8,000 years ago; the Andean and coastal region of Peru and northern Bolivia, ca. 5,000 years ago; and in Mesoamerica, ca. 4,000 years ago.

Moreover, long-range ABMs must be able to generate how, where, and when the four regional systems eventually fused into larger systems until the present state of globalization. For example, whereas the international systems of west and east Asia evolved independently from their period of initial formation up to ca. 1500 bc, and then began sporadic and gradual fusion, both New World systems rapidly fused with the European system 500 years ago through conquest. Just like 21st-century cosmologists have developed detailed models of the early and expanding universe, so someday IR scientists will have available long-range ABMs of the international system. Experience in modeling early polity systems will play a key role, along with new concepts and computational technologies.

Long-range ABMs of the international system will also be able to look into the future, into time-scales when new types of polities will form and evolve, including the first space- and cyber-based polities. Some of these polities will likely have recognizable forms (such as polities with familiar forms of governance institutions) while others will consist of polities purposively evolved for such future environments. If humanity is able to survive the current existential threat of weapons of mass destruction, new forms of polities will be required for spacefaring civilization. ABMs can provide insights and deeper understanding, especially when used in combination with other tools and paradigms available across the sciences.

Acknowledgments

Funding for this study was provided by the Center for Social Complexity and the Program in Computational Social Science at George Mason University, as well as through grants from the U.S. National Science Foundation, the Office of Naval Research, and DARPA. Thanks to Robert Axelrod, Scott Bennett, Stephen Majeski, Scott de Marchi, Juan Fernández-Gracia, Scott Page, Darren Schreiber, Karl Selke, and Nils Weidmann for additional information on some of their models.

References

Alden Smith, E., & Choi, J-K. (2007). The emergence of inequality in small-scale societies: Simple scenarios and agent-based simulations. In T. A. Kohler & S. Van der Leeuw (Eds.), The model-based archaeology of socionatural systems (pp. 105–119). Santa Fe, NM: School for Advanced Research.Find this resource:

    Alt, J. K., Jackson, L. A. J., Hudak, D., & Lieberman, S. (2009). The cultural geography model: Evaluating the impact of tactical operational outcomes on a civilian population in an irregular warfare environment. Journal of Defense Modeling and Simulation: Applications, Methodology, Technology, 6(4), 185–199.Find this resource:

      Altaweel, M. (2015). Settlement dynamics and hierarchy from agent decision-making: A method derived from entropy maximization. Journal of Archaeological Method and Theory, 22, 1122–1150.Find this resource:

        Auble, B. (2010). The Supe Valley model: A preliminary report on an agent-based model to explore the development of prehistoric social complexity in the Supe River Valley, Peru. Proceedings of the Seminar on Origins of Social Complexity. Research Paper. Center for Social Complexity and Department of Computational Social Science. George Mason University, Fairfax, Virginia. Available from the author.Find this resource:

          Auble, B., Magallanes, J., & Cioffi-Revilla, C. (2013). Exploring the development of complex civilization in Ancient Peru using an agent-based model. Proceedings of the Annual Conference of the Society for American Archaeology, April 14, 2013.Find this resource:

            Axelrod, R. (1980a). Effective choice in the Prisoner’s Dilemma. American Political Science Review, 24, 3–25.Find this resource:

              Axelrod, R. (1980b). More effective choice in the Prisoner’s Dilemma. Journal of Conflict Resolution, 24, 379–403.Find this resource:

                Axelrod, R. (1981). The emergence of cooperation among egoists. American Political Science Review, 75(2), 306–318.Find this resource:

                  Axelrod, R. (1984). The evolution of cooperation. New York: Basic Books.Find this resource:

                    Axelrod, R. (1986). An evolutionary approach to norms. American Political Science Review, 80(4), 1095.Find this resource:

                      Axelrod, R. (1987). The evolution of strategies in the Iterated Prisoner’s Dilemma. In L. Davis (Ed.), Genetic algorithms and simulated annealing (pp. 32–41). Los Altos, CA: Morgan Kaufman.Find this resource:

                        Axelrod, R. (1995). A model of the emergence of new political actors. In N. Gilbert & R. Conte (Eds.), Artificial societies: The computer simulation of social life (pp. 19–39). London: University College Press.Find this resource:

                          Axelrod, R. (1997). The dissemination of culture: A model with local convergence and global polarization. Journal of Conflict Resolution, 41(2), 203–226.Find this resource:

                            Axelrod, R., & Bennett, D. S. (1993). A landscape theory of aggregation. British Journal of Political Science, 23(2), 211–233.Find this resource:

                              Axelrod, R., & Dion, D. (1988). The further evolution of cooperation. Science, 242, 1385–1390.Find this resource:

                                Bainbridge, W. S. (2010). The Warcraft Civilization: Social Science in a Virtual World. Cambridge, MA: MIT Press.Find this resource:

                                  Bearce, D. H., & Fisher, E. O. (2002). Economic geography, trade, and war. Journal of Conflict Resolution, 46(3), 365–393.Find this resource:

                                    Bennett, D. S. (2000). Landscapes as analogues of political phenomena. In D. Richards (Ed.), Political complexity: Nonlinear models of politics (pp. 46–79). Ann Arbor: University of Michigan Press.Find this resource:

                                      Bennett, D. S. (2008). Governments, civilians, and the evolution of insurgency: Modeling the early dynamics of insurgencies. Journal of Artificial Societies and Social Simulation, 11(4), article no. 7.Find this resource:

                                        Bhavnani, R. (2006). Agent-based models in the study of ethnic norms and violence. In N. E. Harrison (Ed.), Complexity in world politics (pp. 121–136). Albany: State University of New York Press.Find this resource:

                                          Bhavnani, R. (2008). REsCape: An agent-based framework for modeling resources, ethnicity, and conflict. Journal of Artificial Societies and Social Simulation, 11(2), article no. 7.Find this resource:

                                            Bhavnani, R., & Choi, H. J. (2012). Modeling civil violence in Afghanistan: Ethnic geography, control, and collaboration. Complexity, 17(6), 42–51.Find this resource:

                                              Bhavnani, R., Donnay, K., Miodownik, D., Mor, M., & Helbing, D. (2014). Group segregation and urban violence. American Journal of Political Science, 58(1), 226–245.Find this resource:

                                                Bhavnani, R., & Miodownik, D. (2009). Polarization, ethnic salience, and civil war. Journal of Conflict Resolution, 53(1), 30–49.Find this resource:

                                                  Bogle, G., & Cioffi-Revilla, C. (2016). ZambeziLand: A canonical theory and agent-based model of polity cycling in the Zambezi Plateau, Southern Africa. In J. Barceló & F. Del Castillo (Eds.), Simulating prehistoric and ancient worlds (pp. 359–375). Cham, Switzerland: Springer.Find this resource:

                                                    Bonabeau, E. (2002). Agent-based modeling: Methods and techniques for simulating human systems. Proceedings of the National Academy of Sciences of the United States of America, 99(3), 7280–7287.Find this resource:

                                                      Bondarenko, D., & Korotayev, A. V. (2011). Civilizational models of politigenesis. 2d ed. Saarbrücken, Germany: OmniScriptum/LAP Lambert Academic Publishing.Find this resource:

                                                        Boyle, S., Guerin, S., & Kunkle, D. (2006). An application of multi-agent simulation to policy appraisal in the criminal justice system. In Shu-Heng Chen, Lakhmi Jain, & Chung-Ching Tai (Eds.), Computational economics: A perspective from computational intelligence. Hershey, PA: IGI.Find this resource:

                                                          Bremer, S. A., & Mihalka, M. (1977). Machiavelli in machina: Or politics among hexagons. In Karl W. Deutsch (Ed.), Problems in world modeling. Boston: Ballinger.Find this resource:

                                                            Byrne, D., & Callaghan, G. (2014). Complexity theory and the social sciences. London: Routledge.Find this resource:

                                                              Carley, K. M., Morgan, G. P., & Lanham, M. J. (2016). Deterring the development and use of nuclear weapons: A multi-level modeling approach. Journal of Defense Modeling and Simulation: Applications, Methodology, Technology, 14(1), 95–105.Find this resource:

                                                                Cecconi, F., di Gennaro, E., Parisi, D., & Schiappelli, A. (2004). Protostoria virtuale in Etruria meridionale: simulazione della nascita dei centri protourbani. In N. N. Catacchio (Ed.), Preistoria e protostoria in Etruria: Atti del Sesto Incontro di Studi, Milano 2004 (Vol. 2, pp. 553–560). Milan, Italy: Centro Studi di Preistoria e Archeologia.Find this resource:

                                                                  Cecconi, F., di Gennaro, F., Parisi, D., & Schiappelli, A. (2015). Simulating the emergence of proto-urban centers in ancient Southern Etruria. In J. A. Barcelo & I. Bogdanovic (Eds.), Mathematics and archaeology (pp. 449–463). Boca Raton, FL: CRC Press.Find this resource:

                                                                    Cederman, L-E. (1997). Emergent actors in world politics: How states and nations develop and dissolve. Princeton, NJ: Princeton University Press.Find this resource:

                                                                      Cederman, L-E. (2001). Agent-based modeling in political science. The Political Methodologist, 10(1), 16–22.Find this resource:

                                                                        Cederman, L-E. (2002). Endogenizing geopolitical boundaries with agent-based modeling. Proceedings of the National Academy of Sciences of the United States of America, 99(10), 7296–7303.Find this resource:

                                                                          Cederman, L-E. (2003) Modeling the size of wars: From billiard balls to sandpiles, American Political Science Review, 97(1), 135–150.Find this resource:

                                                                            Cederman, L-E. (2004). Emergent polarity: Analyzing state-formation and power politics. International Studies Quarterly, 38(4), 501–533.Find this resource:

                                                                              Cederman, L-E. (2008) Articulating the geo‐cultural logic of nationalist insurgency. In S. Kalyvas & I. Shapiro (Eds.), Order, conflict, and violence. Cambridge, U.K.: Cambridge University Press.Find this resource:

                                                                                Cederman, L-E., & Girardin, L. (2007a) Beyond fractionalization: Mapping ethnicity on nationalist insurgencies. American Political Science Review, 101, 173–185.Find this resource:

                                                                                  Cederman, L-E., & Girardin, L. (2007b). Toward realistic computational models of civil wars, Paper prepared for presentation at the Annual Meeting of the American Political Science Association, Chicago, August 30–September 2, 2007.Find this resource:

                                                                                    Cederman, L-E., Wimmer, A., & Min, B. (2010). Why do ethnic groups rebel? World Politics, 62(1), 87–119.Find this resource:

                                                                                      Cederman, L-E., Warren, T. C., & Sornette, D. (2011). Testing Clausewitz: Nationalism, mass mobilization, and the severity of war. International Organization, 65(4), 605–638.Find this resource:

                                                                                        Christiansen, J. H., & Altaweel, M. R. (2005). Understanding ancient societies: A new approach using agent-based holistic modeling. Structure and Dynamics: eJournal of Anthropological and Related Sciences, 1(2). Retrieved from http://escholarship.org/uc/item/33w3s07r.Find this resource:

                                                                                          Christiansen, John H., & Altaweel, M. (2006). Simulation of natural and social process interactions: An example from Bronze Age Mesopotamia. Social Science Computer Review, 24(2), 209–226.Find this resource:

                                                                                            Cioffi-Revilla, C. (1989). Mathematical contributions to the scientific understanding of war. In P. E. Johnson (Ed.), Formal theories of politics: Mathematical modelling in political science (pp. 533–545). Oxford: Pergamon.Find this resource:

                                                                                              Cioffi-Revilla, C. (2014). Theoretical nabladot analysis of Amdahl’s Law for agent-based simulations. In L. Lopes et al. (Eds.), Euro-Par 2014 International Workshops, Porto, Portugal, August 25–26, 2014, Revised Selected Papers, Part I (pp. 440–451). Heidelberg, Germany: Springer.Find this resource:

                                                                                                Cioffi-Revilla, C. (2016). Socio-ecological systems. In W. S. Bainbridge & M. C. Roco (Eds.), Handbook of science and technology convergence (pp. 669–689). New York and Heidelberg: Springer.Find this resource:

                                                                                                  Cioffi-Revilla, C. (2017). Introduction to computational social science: Principles and applications (2d ed.). London and Heidelberg: Springer.Find this resource:

                                                                                                    Cioffi-Revilla, C., De Jong, K., & Bassett, J. (2012). Evolutionary computation and agent-based modeling: Biologically-inspired approaches for understanding complex social systems. Computational and Mathematical Organizational Theory, 18(3), 356–373.Find this resource:

                                                                                                      Cioffi-Revilla, C., De Jong, K., Ember, C. R., Luke, S., Abate, T., Crooks, A. T., … Skoggard, I. (2012). MASON RiftLand: An agent-based model for analyzing conflict, disasters, and humanitarian crises in East Africa. Proceedings of the XXII World Congress of the International Political Science Association, Madrid, Spain.Find this resource:

                                                                                                        Cioffi-Revilla, C., & Gotts, N. M. (2003). Comparative analysis of agent-based social simulations: GeoSim and FEARLUS models. Journal of Artificial Societies and Social Systems, 6(4).Find this resource:

                                                                                                          Cioffi-Revilla, C., Honeychurch, W., & Rogers, D. J. (2015). MASON hierarchies: A long-range agent model of power, conflict, and environment in Inner Asia. In J. Bemmann & M. Schmauder (Eds.), Complexity of interaction along the Eurasian Steppe Zone in the First Millennium CE (pp. 89–113). Bonn, Germany: Bonn University Press.Find this resource:

                                                                                                            Cioffi-Revilla, C., Rogers, J. D., Schopf, P., Luke, S., Bassett, J. K., Hailegiorgis, A. B., et al. (2015). MASON NorthLands: A geospatial agent-based model of coupled human-artificial-natural systems in Boreal and Arctic regions. Proceedings of the 2015 Annual Conference of the European Social Simulation Association, Groningen, Netherlands. Available at https://www.researchgate.net/publication/280623228.Find this resource:

                                                                                                              Cioffi-Revilla, C., Rogers, J. D., Wilcox, S., & Alterman, J. (2011). Computing the Steppes: Data analysis for agent-based models of polities in Inner Asia. In U. Brosseder & B. Miller (Eds.), Xiongnu Archaeology: Multidisciplinary perspectives of the first steppe empire in Inner Asia (pp. 97–110). Bonn, Germany: Bonn University Press.Find this resource:

                                                                                                                Cioffi-Revilla, C., & Rouleau, M. (2009a). MASON AfriLand: A regional multi-country agent-based model with cultural and environmental Dynamics. Proceedings of the Human Behavior-Computational Modeling and Interoperability Conference 2009 HB-CMI-09, Joint Institute for Computational Science, Oak Ridge National Laboratory, Oak Ridge, Tennessee, June 23–24, 2009. Available at https://cs.gmu.edu/~eclab/projects/mason/publications/afriland09.pdf.Find this resource:

                                                                                                                  Cioffi-Revilla, C., & Rouleau, M. (2009b). MASON AfriLand: A regional multi-country agent-based model with cultural and environmental dynamics. Paper presented at the Annual Conference of the Peace Science Society, Chapel Hill, North Carolina.Find this resource:

                                                                                                                    Cioffi-Revilla, C., & Rouleau, M. (2010). MASON RebeLand: An agent-based model of politics, environment, and insurgency. International Studies Review, 12(1), 31–46.Find this resource:

                                                                                                                      Collins, A., Sokolowski, J., & Banks, C. (2013). Applying reinforcement learning to an insurgency Agent-based Simulation. Journal of Defense Modeling and Simulation: Applications, Methodology, Technology, 11(4), 353–364.Find this resource:

                                                                                                                        Conte, R., Gilbert, G. N., Bonelli, G., Cioffi-Revilla, C., Deffaunt, G., Kertesz, J., et al. (2012). Manifesto of computational social science. European Physical Journal Special Topics, 214, 325–346.Find this resource:

                                                                                                                          Cusack, T. R., & Stoll, R. J. (1990). Exploring realpolitik: Probing international relations theory with computer simulation. Boulder, CO: Lynne Rienner.Find this resource:

                                                                                                                            Degterev, D. A. (2016). Dissemination of cultural norms and values: Agent-based modeling. Vestnik RUDN. International Relations, 16(1), 141–152.Find this resource:

                                                                                                                              Delligatti, L. (2014). SysML distilled: A brief guide to the systems modeling language. Upper Saddle River, NJ: Addison-Wesley.Find this resource:

                                                                                                                                Doran, James E., & Palmer, M. (1995). The EOS project: Integrating two models of Paleolithic social change. In N. Gilbert & R. Conte (Eds.), Artificial societies: The computer simulation of social life (pp. 103–125). London: UCL.Find this resource:

                                                                                                                                  Doran, J. E., Palmer, M., Gilbert, N., & Mellars, P. (1994). The EOS project: Modelling Upper Paleolithic social change. In Nigel Gilbert & Jim E. Doran (Eds.), Simulating Societies (pp. 195–221). London: UCL.Find this resource:

                                                                                                                                    Dover, Thomas J. (2013). Implementing politogenesis as an agent-based model in a circumscribed environment. Proceedings of the Fall 2013 Seminar on Origins of Social Complexity. Research Paper. Center for Social Complexity and Department of Computational Social Science, George Mason University.Find this resource:

                                                                                                                                      Dover, T. J., & Cioffi-Revilla, C. (2015). Implementing politogenesis: An agent-based model of canonical cycling in a circumscribed environment. Proceedings of the 80th Annual Meeting of the Society for American Archaeology, San Francisco, CA.Find this resource:

                                                                                                                                        Duffy, G. (1992). Concurrent interstate conflict simulations: Testing the effects of the serial assumption. Mathematical and Computer Modelling, 16, 241–270.Find this resource:

                                                                                                                                          Duffy, G. (1993). Historical reflection and the outcomes of war: A massively parallel computer simulation. Paper presented at the Annual Meeting of the International Studies Association, Acapulco, Mexico.Find this resource:

                                                                                                                                            Edmonds, B., & Moss, S. (2005). From KISS to KIDS–An “antisimplistic” modelling approach. In P. Davidsson, B. Logan, & T. Keiki (Eds.), Multi-agent and Multi-agent-based simulation (pp. 130–144). Berlin Heidelberg: Springer.Find this resource:

                                                                                                                                              Epstein, J. M. (1999). Agent-based computational models and generative social science. Complexity, 4(5), 41–60.Find this resource:

                                                                                                                                                Epstein, J. M. (2002). Modeling civil violence: An agent-based computational approach. Proceedings of the National Academy of Sciences of the United States of America, 99(3); 7243–7250.Find this resource:

                                                                                                                                                  Freidenthal, S., Moore, A., & Steiner, R. (2015). A practical guide to SysML: The systems modeling language. Amsterdam, The Netherlands: Elsevier.Find this resource:

                                                                                                                                                    Gartzke, E., & Weisiger, A. (2013). Fading friendships: Alliances, affinities and the activation of international identities. British Journal of Political Science, 43(1), 25–52.Find this resource:

                                                                                                                                                      Gavrilets, S., Anderson, D. G., & Turchin, P. (2010). Cycling in the complexity of early societies. Cliodynamics: Journal of Theoretical and Mathematical History, 1(1), 58–80.Find this resource:

                                                                                                                                                        Gilbert, N., & Troitzsch, K. (2005). Simulation for the social scientist. 2d ed. Buckingham, U.K., and Philadelphia: Open University Press.Find this resource:

                                                                                                                                                          Goh, C. K., Quek, H. Y., Tan, K. C., & Abbass, H. A. (2006). Modeling civil violence: An evolutionary multi-agent, game theoretic approach. In Proceedings of the 2006 IEEE International Conference on Evolutionary Computation, 1624–1631. Available at http://ieeexplore.ieee.org/document/1688503.Find this resource:

                                                                                                                                                            Griffin, A. F. (2011). Emergence of fusion/fission cycling and self-organized criticality from a simulation model of early complex polities. Journal of Archaeological Science, 38(4), 873–883.Find this resource:

                                                                                                                                                              Griffin, A. F., & Stanish, C. (2007). An agent-based model of settlement patterns and political consolidation in the Lake Titicaca Basin of Peru and Bolivia. Structure and Dynamics: eJournal of Anthropological and Related Sciences, 2(2). Available online.Find this resource:

                                                                                                                                                                Grinin, L. E. (2009). The pathways of politogenesis and models. Social Evolution & History: Studies in the Evolution of Human Societies, 8(1), 92–132.Find this resource:

                                                                                                                                                                  Grinin, L. E., & Korotayev, A. V. (2009). The epoch of the initial politogenesis. Social Evolution & History: Studies in the Evolution of Human Societies, 8(1), 52–91.Find this resource:

                                                                                                                                                                    Harrison, J. F. (2016). A General Social Agent-Based Model of Opinion Dynamics with Applications to STEM Education and Radicalization (PhD diss.). George Mason University, Fairfax, VA 22030 USA.Find this resource:

                                                                                                                                                                      Heckbert, S. (2013). MayaSim: An agent-based model of the ancient Maya social-ecological system. Journal of Artificial Societies and Social Simulation, 16(4), 11.Find this resource:

                                                                                                                                                                        Hoffmann, M. J. (2005). Ozone depletion and climate change: Constructing a global response. Albany: State University of New York Press.Find this resource:

                                                                                                                                                                          Hoffmann, M. J. (2006). Beyond regime theory: Complex adaptation and the ozone depletion regime. In N. E. Harrison (Ed.), Complexity in world politics: Concepts and methods of a new paradigm (pp. 95–119). Albany: State University of New York Press.Find this resource:

                                                                                                                                                                            Hoffmann, M. J. (2008). Agent-based modeling. In A. Klotz & D. Prakash (Eds.), Qualitative methods in international relations: A pluralist guide (pp. 187–208): London: Palgrave Macmillan.Find this resource:

                                                                                                                                                                              Ilachinski, A. (1997). Irreducible semi-autonomous adaptive combat (ISAAC): An artificial life approach to land warfare. Center for Naval Analysis CNA Research Memorandum CRM 97–61. Alexandria, VA.Find this resource:

                                                                                                                                                                                Ilachinski, A. (2004). Artificial war: Multi-agent based simulation of combat. Singapore: World Scientific.Find this resource:

                                                                                                                                                                                  Ilachinski, A. (2005). Self-organized terrorist-counterterrorist adaptive coevolutions, Part I: A conceptual design. CRM D0010776.A3/1Rev. Alexandria, VA: Center for Naval Analyses CNA.Find this resource:

                                                                                                                                                                                    Ilachinski, A. (2012). Modelling insurgent and terrorist networks as self-organised complex adaptive systems. International Journal of Parallel, Emergent and Distributed Systems, 27(1), 45–77.Find this resource:

                                                                                                                                                                                      Johnson, D. D. P., Weidmann, N. B., & Cederman, L-E. (2011). Fortune favours the bold: An agent-based model reveals adaptive advantages of overconfidence in war. PLOS One, 6(6), e20851.Find this resource:

                                                                                                                                                                                        Keller, J. P., Desouza, K. C., & Lin, Y. (2010). Dismantling terrorist networks: Evaluating strategic options using agent-based modeling. Technological Forecasting and Social Change, 77, 1014–1036.Find this resource:

                                                                                                                                                                                          Kennedy, W. G., Cotla, C. R., Gulden, T., Coletti, M., & Cioffi-Revilla, C. (2012). Validation of a household agent-based model of the societies of East Africa. Proceedings of the 2012 Human, Social, Cultural, and Behavioral Conference, San Francisco, United States.Find this resource:

                                                                                                                                                                                            Kennedy, W. G., Cotla, C. R., Gulden, T., Coletti, M., & Cioffi-Revilla, C. (2014). Towards validating a model of households and societies of East Africa. In S. H. Chen, I. Terano, H. Yamamoto, & Chung-Ching Tai (Eds.), Advances in computational social science: Post-Proceedings of the Fourth World Congress in Social Simulation, Taipei, Taiwan (pp. 315–328). Tokyo and Heidelberg: Springer.Find this resource:

                                                                                                                                                                                              Kennedy, W. G., Gulden, T., Hailegiorgis, A. B., Bassett, J., Coletti, M., Balan, & Gabriel C., et al. (2010, September 6–9). An agent-based model of conflict in East Africa and the effect of the privatization of land. Proceedings of the 3rd World Congress in Social Simulation, Kassel, Germany.Find this resource:

                                                                                                                                                                                                Kohler, T. A., Bocinsky, R. K., Cockburn, D., Crabtree, S. A., Varien, M. D., & Kolm, K. E., et al. (2012a). Modelling prehispanic Pueblo societies in their ecosystems. Ecological Modeling, 241(24), 30–41.Find this resource:

                                                                                                                                                                                                  Kohler, T. A., Cockburn, D., Hooper, P. L., Bocinsky, R. K., & Kobti, Z. (2012b). The coevolution of group size and leadership: An agent-based public goods model for prehispanic pueblo societies. Advances in Complex Systems, 15(1 and 2), 115007. Available online.Find this resource:

                                                                                                                                                                                                    Kuznar, L. A., Sedlmeyer, R. L., & Kreft, A. (2008). NOMAD: An Agent-based Model of Nomadic Pastoralist/Sedentary Peasant Interaction. In H. Barnard & W. Wendrich (Eds.), The Archaeology of Mobility: Old World and New World Nomadism (pp. 447-583). Los Angeles, CA: Cotsen Institute of Archaeology, University of California.Find this resource:

                                                                                                                                                                                                      Liu, J., Dietz, T., Carpenter, S. R., Alberti, M., Folke, C., & Moran, E., et al. (2007). Complexity of coupled human and natural systems. Science, 317(5844), 1513–1516.Find this resource:

                                                                                                                                                                                                        Luteijn, R. (2015). Exploration of paths to major power war (PhD thesis, Technical University of Delft, Delft, The Netherlands). Available at https://repository.tudelft.nl/islandora/object/uuid:0867f344-5a04-44b8-8cdc-0211d702fe79/datastream.Find this resource:

                                                                                                                                                                                                          MacKerrow, E. P. (2003). Understanding why: Dissecting radical Islamist terrorism with agent-based simulation. Los Alamos Science, 28, 184–191.Find this resource:

                                                                                                                                                                                                            Majeski, S. J. (2004). Asymmetric power among agents and the generation and maintenance of cooperation in international relations. International Studies Quarterly, 48(2), 455–470.Find this resource:

                                                                                                                                                                                                              Majeski, S. J. (2005). Do exploitive agents benefit from asymmetric power in international politics? British Journal of Political Science, 35(4), 745–755.Find this resource:

                                                                                                                                                                                                                Makowsky, M. D., & Rubin, J. (2013). An agent-based model of centralized institutions, social network technology, and revolution. PLOS One, 8(11), e80380.Find this resource:

                                                                                                                                                                                                                  Malkov, A. S. (2004). Spatial modeling of historical dynamics. Proceedings of the International Conference on Mathematical Modelling of Social and Economical Dynamics, June 23–35, 2004, Moscow, Russia.Find this resource:

                                                                                                                                                                                                                    Malkov, A. S. (2006). The Silk Roads: A mathematical model. In L. Grinin, P. Turchin, V. C. de Munck, & A. Korotayev (Eds.), History and mathematics: Historical dynamics and development of complex societies. Moscow, Russia: KomKniga.Find this resource:

                                                                                                                                                                                                                      Masad, D. P. (2013). The emergence of new geopolitical actors: Replicating and expanding the Axelrod Tribute Model. Proceedings of the Fall 2013 Seminar on Origins of Social Complexity. Center for Social Complexity and Department of Computational Social Science, George Mason University. Fairfax, VA.Find this resource:

                                                                                                                                                                                                                        Masad, D. P. (2016). Agents in conflict: Comparative agent-based modeling of international crises and conflicts (PhD diss.). George Mason University, Fairfax, VA.Find this resource:

                                                                                                                                                                                                                          McFarlane, H. J. (2016). An agent based model of community authority structure resilience. (PhD diss.). George Mason University, Fairfax, VA.Find this resource:

                                                                                                                                                                                                                            Min, B. W. (2002). Trade and war in cellular automata worlds: A computer simulation of interstate interactions (PhD diss.). The Ohio State University, Columbus, OH.Find this resource:

                                                                                                                                                                                                                              Min, B. W., Pollins, B. M., & Lebow, R. N. (2004). War, trade, and power laws in a simulated world. Paper presented at the Power Laws in the Social Sciences, Center for Social Complexity, George Mason University.Find this resource:

                                                                                                                                                                                                                                Ostrom, E. (2009). A general framework for analyzing sustainability of socio-ecological Systems. Science, 325, 419–422.Find this resource:

                                                                                                                                                                                                                                  Page, S. E. (2015). What sociologists should know about complexity. American Sociological Review, 41(1), 21–41.Find this resource:

                                                                                                                                                                                                                                    Paravantis, J. A. (2016). From Game Theory to Complexity, Emergence and Agent-Based Modeling in World Politics. In G. A. Tsihrintzis et al. (Eds.), Intelligent Computing Systems (pp. 39–85). Berlin and Heidelberg, Germany: Springer-Verlag.Find this resource:

                                                                                                                                                                                                                                      Pugacheva, E. (2016). Collective behavior as a new social agent. In P. Arhrweiler, N. Gilbert, & A. Pyka (Eds.), Joining complexity science and social simulation for innovation policy: Agent-based modelling using the SKIN Platform (pp. 350–369). Newcastle-upon-Tyne, U.K.: Cambridge Scholars.Find this resource:

                                                                                                                                                                                                                                        PSSC (Physical Sciences Study Committee). (1960). Misconceptions in the Physical Sciences. Washington, DC: National Research Council.Find this resource:

                                                                                                                                                                                                                                          Railsback, S. F., & Grimm, V. (2012). Agent-based and individual-based modeling: A practical introduction. Princeton, NJ: Princeton University Press.Find this resource:

                                                                                                                                                                                                                                            Rogers, D. J. (2017). Dynamic trajectories, adaptive cycles, and complexity in culture change. Journal of Archaeological Method and Theory, 1–30.Find this resource:

                                                                                                                                                                                                                                              Rouleau, M. (2011). A computational theory of endogenous norm emergence: The NormSim agent-based model in MASON (Unpublished PhD diss.), George Mason University, Fairfax, VA.Find this resource:

                                                                                                                                                                                                                                                Selke, K. D. (2004). Learning to think strategically: An examination of a strategic-operational wargame named “Conflict” (Unpublished senior thesis). Lake Superior State University, Michigan.Find this resource:

                                                                                                                                                                                                                                                  Selke, K. D. (2017). RealLand: 21st century EARTH pivoting towards representational modeling (PhD diss.). George Mason University, Fairfax, Virginia.Find this resource:

                                                                                                                                                                                                                                                    Simon, H. A. (1996). The sciences of the artificial (3d ed.). Cambridge, MA: MIT Press.Find this resource:

                                                                                                                                                                                                                                                      Simon, M. V., & Starr, H. (2000). Two-level security management and the prospects for new democracies: A simulation analysis. International Studies Quarterly, 44, 391–422.Find this resource:

                                                                                                                                                                                                                                                        Stanish, C., & Levine, A. (2011). War and early state formation in the northern Titicaca Basin, Peru. Proceedings of the National Academy of Science of the U.S.A., 108(34), 13901–13906.Find this resource:

                                                                                                                                                                                                                                                          Sylvan, D., & Majeski, S. (2002). Was Luce right? Simulating the growth of U.S. client states. Paper presented at the Annual Convention of the International Studies Association, New Orleans, United States.Find this resource:

                                                                                                                                                                                                                                                            Sylvan, D., & Majeski, S. (2003). An agent-based model of the acquisition of U.S. client states. Paper presented at the 44th Annual Convention of the International Studies Association, Portland, United States.Find this resource:

                                                                                                                                                                                                                                                              Sutherland, B. (2012). The science of civil war: What makes heroic strife. The Economist, April 21.Find this resource:

                                                                                                                                                                                                                                                                Taber, C. S., & Timpone, R. J. (1996). Computational modeling. Thousand Oaks, CA: SAGE.Find this resource:

                                                                                                                                                                                                                                                                  Turchin, P. (2003). Historical dynamics: Why states rise and fall. Princeton, NJ: Princeton University Press.Find this resource:

                                                                                                                                                                                                                                                                    Turchin, P., Currie, T. E., Turner, E. A. L., & Gavrilets, S. (2013). War, space, and the evolution of Old World complex societies. Proceedings of the National Academy of Sciences of the U.S.A., 110(41), 16384–16389.Find this resource:

                                                                                                                                                                                                                                                                      Ulloa, R., Kacperski, C., & Sancho, F. (2016). Institutions and cultural diversity: Effects of democratic and propaganda processes on local convergence and global diversity. PLoS one, 11(4), e0153334.Find this resource:

                                                                                                                                                                                                                                                                        van Creveld, M. (2013). Wargames: From gladiators to gigabytes. Cambridge, U.K.: Cambridge University Press.Find this resource:

                                                                                                                                                                                                                                                                          Weidmann, N. B. (2016). Micro-cleavages and violence in civil wars: A computational assessment. Conflict Management and Peace Science, 33(5), 539–558.Find this resource:

                                                                                                                                                                                                                                                                            Weidmann, N. B., & Salehyan, I. (2013). Violence and ethnic segregation: A computational model applied to Baghdad. International Studies Quarterly, 57, 52–64.Find this resource:

                                                                                                                                                                                                                                                                              Wilkinson, T. J., Christiansen, J. H., Ur, J., Widell, M., & Altaweel, M. (2007). Urbanization within a dynamic environment: Modeling Bronze Age communities in Upper Mesopotamia. American Anthropologist, 109(1), 52–68.Find this resource:

                                                                                                                                                                                                                                                                                Wohlstetter, A. (1959). The delicate balance of terror. Foreign Affairs, 37(1), 211–234.Find this resource:

                                                                                                                                                                                                                                                                                  Wohlstetter, A. (1968). Theory and opposed-systems design. Journal of Conflict Resolution, 12(3), 302–331.Find this resource:

                                                                                                                                                                                                                                                                                    Wu, J., & Axelrod, R. (1995). How to cope with noise in the iterated Prisoner’s Dilemma. Journal of Conflict Resolution, 39(1), 183–189.Find this resource:

                                                                                                                                                                                                                                                                                      Zinnes, D. A., & Gillespie, J. V. (Eds.). (1976). Mathematical models of international relations. New York: Praeger.Find this resource:

                                                                                                                                                                                                                                                                                        Zinnes, D. A., Gillespie, J. V., & Tahim, G. S. (1978). A formal analysis of some issues in balance of power theories. International Studies Quarterly, 22(3), 323–356.Find this resource:

                                                                                                                                                                                                                                                                                          Zinnes, D. A., & Muncaster, R. G. (1987). Transaction flows and integrative processes. In C. Cioffi-Revilla, R. L. Merritt, & D. A. Zinnes (Eds.), Communication and interaction in global politics. Beverly Hills, CA: SAGE.Find this resource: