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date: 19 September 2017

Empirical Analyses of Deterrence

Summary and Keywords

Deterrence is an important subject, and its study has spanned more than seven decades. Much research on deterrence has focused on a theoretical understanding of the subject. Particularly important is the distinction between classical deterrence theory and perfect deterrence theory. Other studies have employed empirical analyses. The empirical literature on deterrence developed at different times and took different approaches. The early empirical deterrence literature was highly limited for varying reasons. Much of the early case study literature did not seek to test deterrence theory. Early quantitative studies did seek to do so, but they were hampered by rudimentary methods, poor research design, and/or a disconnect between quantitative studies and formal theories of deterrence. Modern empirical research on deterrence has made great strides toward bridging the formal-quantitative divide in the study of deterrence and conducting theoretically driven case studies. Further, researchers have explored the effect of specific variables on deterrence, such as alliances, reputations and credibility, and nuclear weapons. Future empirical studies of deterrence should build on these modern developments. In addition, they should build on perfect deterrence theory, given its logical consistency and empirical support.

Keywords: deterrence, empirical analysis, international conflict, rational choice theory, perfect deterrence theory, quantitative analysis, case studies, empirical international relations theory


Deterrence is the use of a threat by one party in an attempt to prevent another from challenging the status quo. It is an important subject, and its study has spanned more than seven decades. Much of this literature has focused on the development of deterrence theory. Deterrence theory has largely been game theoretic in nature, although some theoretical developments have been non-formal. There has been an extensive amount of empirical literature on deterrence as well, which is the focus of this article. While the emphasis here is on the empirical literature, some examination of the theoretical literature is needed to assess the empirical analyses properly.

The article continues with a discussion of the broad relevance of deterrence and the distinction between general and immediate deterrence. It then reviews early empirical analyses of deterrence before discussing deterrence theory and the traditional divide between deterrence theory and empirical analysis. The discussion ends with an analysis of modern empirical developments in the study of deterrence.

The Continuing Relevance of Deterrence

When thinking about deterrence, people tend to think about nuclear weapons, crises, or both. At first glance, each connection seems perfectly justified. After all, although World War II was the most destructive war in history, the atomic bombs dropped on Japan in August 1945 introduced an unprecedented level of destructive power. Observers quickly realized that the enormous costs of nuclear weapons compared to conventional ones revolutionized warfare in many ways. Once thermonuclear weapons were introduced in 1952, the destructive power increased by orders of magnitude. Warheads as large as 25 megatons (million tons) of 2,4,6-trinitrotoluene (TNT) were deployed by the United States and the former Soviet Union during the Cold War.1 Given this massive power, all-out nuclear war threatened the very existence of life on Earth, making “winning” such a war virtually useless. Therefore, states would have to rely on threats of retaliation to dissuade others from taking certain actions. Scholars such as Brodie (1946) argued that armed forces now existed to deter wars rather than to win them.

An oft-touted case of successful deterrence is the Cuban Missile Crisis, which occurred between the United States and Soviet Union in October 1962.2 The crisis was probably the closest the world has come to nuclear war, and President John F. Kennedy estimated the chances of nuclear war as “between one out of three and even.” However, war was successfully avoided as the Soviets backed down in the face of an American naval quarantine. As U.S. secretary of state Dean Rusk stated, “we were eyeball to eyeball and the other guy just blinked.” Although deterrence seemed to work in the Cuban Missile Crisis, in other crises it has failed. For example, in the July Crisis of 1914, deterrence failed all around, and a dispute between Austria-Hungary and Serbia over the assassination of the Archduke Franz Ferdinand, heir to the Austrian throne, by Serbian nationalist Gavrilo Princip boiled over into World War I.

While deterrence is certainly relevant to understanding nuclear weapons and crises in international relations, deterrence is by no means limited to these areas. States are not solely interested in deterring nuclear attacks against them, nor do they rely only on threats of nuclear retaliation to deter challenges. States also have strong incentives to deter conventional attacks on themselves and their allies. For example, in the July Crisis that led to World War I, each of the major powers tried to deter intervention by other major powers (Zagare, 2011). Conventional deterrence has also played an important role in relations between Israel and Arab states (Shimshoni, 1988; Sorokin, 1994), as well as numerous other cases. Furthermore, states do not wait until crises arise before trying to deter attacks against them or challenges to the status quo. To see this clearly, it is important to consider the distinction between general and immediate deterrence.

General and Immediate Deterrence

There are multiple ways that deterrence can be classified. There are two types of deterrent threats, based on the potential target of attack. The purpose of direct deterrence is to deter a direct attack on the defender. The goal of extended deterrence, conversely, is to deter attack on one’s allies. We can also distinguish between general deterrence, which relates to deterrence within everyday relationships between states, and immediate deterrence, which relates to last-ditch attempts at deterrence within crises (Morgan, 1983). Huth (1988) combines these two kinds of deterrence situations with the two types of deterrent threats to form four categories of deterrence: direct-immediate deterrence, direct-general deterrence, extended-immediate deterrence, and extended-general deterrence. Much of the empirical literature has focused on extended-immediate deterrence.

General deterrence is much broader than immediate deterrence. For example, consider a case of immediate deterrence such as the Cuban Missile Crisis. Studies of immediate deterrence seek to understand how escalation can be controlled within the context of a crisis. That is, once a state has already challenged the status quo, how can a defending state deter the challenger from taking further action and thus avoid all-out war? Successful immediate deterrence entails a challenger’s backing down following the defender’s threat to retaliate, whereas the failure of immediate deterrence results in the challenger’s attacking despite the defender’s retaliatory threat.

While in one light, the Cuban Missile Crisis was a deterrence success and the July Crisis was a deterrence failure, both were crises. Indeed, many studies of deterrence have focused their attention squarely on crises, particularly within early empirical studies of deterrence. However, deterrence is relevant in many cases beyond crises. Furthermore, focusing exclusively on crises creates a distorted, incomplete, and inaccurate understanding of deterrence (Achen & Snidal, 1989; Fearon, 2002). Revisiting the comparison of the Cuban Missile and July Crises, one could easily consider both cases to be deterrence failures because they were both crises. The need for immediate deterrence indicates that general deterrence has previously failed (Danilovic, 2001a). If general deterrence always succeeds, crises and wars do not occur. It is important, then, to focus on the origins of international crises, not just the management of those crises.

Since general deterrence necessarily precedes immediate deterrence, the analysis of general deterrence is more important for a general understanding of international conflict than the analysis of immediate deterrence (Quackenbush, 2011b; Morgan, 2003). Furthermore, as the literature on selection bias (e.g., Fearon, 2002; Reed, 2000) makes clear, examination of immediate deterrence without consideration of the origins of immediate deterrence cases (i.e., the failure of general deterrence) can lead to misleading empirical results.

Nonetheless, the early empirical literature on deterrence (both quantitative analysis and case studies) focused almost exclusively on immediate deterrence. As Huth (1999, p. 27) states, the “empirical study of general deterrence is less extensive and less well developed than is the body of work on immediate deterrence.” This is unfortunate because “general deterrence is a situation much more typical of international politics” and immediate deterrence is “a type of situation that seldom exists” (Morgan, 1983, pp. 42, 45). To see this more clearly, we now turn our attention to early empirical studies of deterrence.

Early Empirical Analyses

As with other areas of political science, two empirical approaches have been used in deterrence literature: case studies and quantitative analysis.3 The case study literature has focused on in-depth analyses of particular deterrence situations, whereas quantitative studies have employed large-N statistical analyses of deterrence cases. Each of these research areas has generally focused on crisis situations within extended-immediate deterrence.

Early Deterrence Case Studies

One of the earliest efforts to conduct a wide-ranging analysis of deterrence cases was by George and Smoke (1974). They examine deterrence in American foreign policy through case studies of a series of 11 Cold War crises, including the Berlin blockade in 1948, the outbreak of the Korean War in 1950, the Taiwan Straits Crisis in 1954–1955, the Cuban Missile Crisis in 1962, and several others. Through the course of their study, George and Smoke (1974) identify three basic patterns of deterrence failure: the fait accompli attempt, the limited probe, and controlled pressure.

Other scholars have examined deterrence by various other countries, not only the United States. For instance, Whiting (1968) examines Chinese deterrence within the context of the Korean War. In a subsequent study, Whiting (1975) examines the Chinese practice of deterrence, particularly in the cases of India (in the context of the 1962 Indo-Chinese War) and Indochina (in the context of the Vietnam War). Others have focused on cases of deterrence by other countries, such as in the context of Arab-Israeli relations (e.g., Lieberman, 1994, 1995; Shimshoni, 1988).

Probably the most prolific scholars within this literature were Lebow and Stein. Lebow (1981) examines deterrence within crises such as the July Crisis, the Fashoda Crisis, and the Cuban Missile Crisis. He argues that cognitive closure and misperception are common and undermine deterrence. In a follow-on study, Lebow (1984) tried to assess whether states jump through windows of opportunity presented by shifts in military capabilities. He examined three cases: Germany in 1914, the United States from 1948–1960, and the Soviet Union from 1982–1986. He concludes that states do not make their decisions solely on the basis of power. Jervis, Lebow, and Stein (1985) examine a wide range of deterrence cases, including between Egypt and Israel, between Argentina and the United Kingdom, and the July Crisis of 1914. They argue that various psychological and cognitive limitations interfere with rationality and thus undermine the application of rational choice theory that is so common within deterrence theory. Furthermore, Lebow and Stein (1994) examine the Cuban Missile Crisis of 1962 and the Alert Crisis of 1973 to argue that, rather than helping to preserve peace, deterrence lengthened the Cold War.

Many of these case studies are part of efforts to uncover general patterns from the cases examined. However, much less attention is paid to either testing specific theories of deterrence or examining the generalities revealed by other case studies. Nonetheless, the case-study literature is also known for its criticisms of deterrence theory. In many ways, these criticisms of deterrence theory are criticisms of realism. And this makes some sense since classical deterrence theory is closely connected to realism (Zagare, 2011). Further, arguments within the case-study literature that deterrence is dangerous (e.g., Lebow & Stein, 1994) are similar to criticisms by others that realism is not only wrong, it is dangerous (e.g., Senese & Vasquez, 2008). However, deterrence theory is not equivalent to realism; in particular, perfect deterrence theory argues against realism (Zagare, 2011).

Two other primary criticisms of rational deterrence theory were made by the case study literature. One group of studies (e.g., Lebow, 1981; Jervis, Lebow, & Stein, 1985; Steinbruner, 1976) takes issue with the notion of rationality. Another group of studies (e.g., George & Smoke, 1974) essentially takes issue with the nature of deductive theory. However, each argument is flawed (Wagner, 1992). The psychological argument falls through once instrumental rationality is properly understood (Quackenbush, 2004); the argument regarding the historical detail of deterrence situations relies on a flawed understanding of deductive theory and the logic of explanation. In addition, case studies have focused mostly on immediate deterrence, limiting their utility for understanding deterrence more broadly. Furthermore, the case study literature has been plagued with a variety of problems in the areas of concept formation, selection bias, and lack of generalization (Achen & Snidal, 1989; Huth & Russett, 1990), which has greatly reduced its utility for a general understanding of deterrence.

Early Deterrence Quantitative Studies

The quantitative empirical literature on deterrence has examined the question of when deterrent threats work using large-N quantitative analysis. Like the case study literature, the focus of these studies has been almost exclusively on extended-immediate deterrence. A great deal of work has been devoted to refining the population of extended-immediate deterrence cases.

The earliest quantitative analyses of deterrence appeared in the 1960s. Russett (1963, 1967) began with rudimentary analyses of small numbers of cases. Fink (1965) further examined Russett’s data through a series of cross-tabulations. The data and methodology of these initial studies were quite rudimentary. An important step forward was taken by Karsten, Howell, and Allen (1984), who conducted a wide-ranging quantitative analysis of the effectiveness of military threats. They examined more than 100 variables, but their research design was badly flawed, placing serious constraints on the utility of their study.

Certainly the most notable early quantitative studies of deterrence were by Russett and Huth. Huth and Russett (1984) conduct a much more sophisticated quantitative analysis of extended immediate deterrence using probit methods. They find that the local balance of forces is one of the most important determinants of deterrence success. Huth and Russett (1988) build on that analysis to examine the likelihood that the defender carries out its threat if deterrence fails. They find that defenders are more likely to fight if they are contiguous with or allied to the protégé and when the short-term balance of forces is in their favor. Huth (1988) builds on these quantitative studies and includes a variety of case studies as well.

Wu (1990) seeks to improve on Huth and Russett’s studies by placing greater focus on the credibility of the defender’s retaliatory threat. However, his empirical analysis is quite rudimentary. Huth, Gelpi, and Bennett (1993) examine cases of both direct and extended deterrence, although they maintain a focus on immediate deterrence. They find that rational deterrence theory enjoys much better empirical support than structural realism. Huth and Russett (1993) provide one of the rare analyses of general deterrence within the early literature. They use enduring rivalries to identify cases of general deterrence, but their findings are preliminary.

There were a variety of important limitations in the early empirical literature. Not only were there a variety of methodological issues, but more important, these early empirical deterrence studies were limited in their ability to test deterrence theory. Theories are useful to the extent that they help to understand and explain reality, so empirical testing is needed for determining the usefulness of deterrence theory (Harvey, 1998). But there is a divide separating deterrence theory from these early empirical analyses of deterrence. To see this point, it is important to examine the two main theories of deterrence: classical deterrence theory and perfect deterrence theory.

Deterrence Theory

Deterrence theory—often called rational deterrence theory—argues that in order to deter attacks, a state must persuade potential attackers that (a) it has an effective military capability, (b) it could impose unacceptable costs on an attacker, and (c) the state would carry out its threat if attacked (Kaufmann, 1956). So deterrence theorists have attempted to explain deterrence through several key elements: “the assumption of a very severe conflict, the assumption of rationality, the concept of a retaliatory threat, the concept of unacceptable damage, the notion of credibility, and the notion of deterrence stability” (Morgan, 2003, p. 8).

Some scholars (e.g., Morgan, 2003) argue that while we can distinguish between different deterrence strategies, there is only one deterrence theory. Others (e.g., Quackenbush, 2011a; Quackenbush & Zagare, 2016) identify different theories of deterrence, focusing in particular on the distinction between classical deterrence theory and perfect deterrence theory.4 Much of the deterrence literature can be categorized under a single theory: classical deterrence theory. Further, because theoretical approaches and assumptions vary widely from one theorist to another, we can divide classical deterrence theory into two subgroups: structural deterrence theory and decision-theoretic deterrence theory (Zagare, 1996).

Structural deterrence theory, closely aligned with realism, argues that a balance of power brings peace; if two states have equal power, each will be deterred since neither will be able to gain an advantage (e.g., Kaufmann, 1956; Brodie, 1959; Intriligator & Brito, 1984, 1987; Mearsheimer, 1990). Furthermore, structural deterrence theory argues that nuclear deterrence is inherently stable. While “in a conventional world, a country can sensibly attack if it believes that success is probable,” with nuclear weapons, “a nation will be deterred from attacking even if it believes that there is only a possibility that its adversary will retaliate” (Waltz, 1988, p. 626). Thus, the key to deterrence is a second-strike capability, and once this is achieved (Wohlstetter, 1959), deterrence is straightforward since the enormous costs associated with nuclear war make an attack irrational. Accidental war, then, represents the only real threat to deterrence.

Decision-theoretic deterrence theorists, on the other hand, utilize expected utility and game theory to construct models of deterrence (e.g., Schelling, 1960, 1966; Brams & Kilgour, 1988; Powell, 1990, 2003).5 While their approach is quite different, decision-theoretic deterrence theorists take to heart the structural deterrence theorists’ idea that nuclear war is irrational by assuming that conflict is always the worst outcome.

A typical classical model of deterrence is shown in Figure 1. In this game, there are two actors: a Challenger, who seeks to alter the status quo; and a Defender, who seeks to deter such challenges. Challenger begins the game by deciding whether to cooperate, in which case the Status Quo remains, or to attack Defender by choosing to defect. Defender, in turn, has two possible responses to a challenge: to concede, resulting in Defender Concedes; or to defy, resulting in Conflict. Challenger would most prefer Defender Concedes, and Defender likes Status Quo the best. However, both agree that Conflict is the worst possible outcome.

Empirical Analyses of DeterrenceClick to view larger

Figure 1. ‘Classical’ Deterrence Game.

Defender faces a quandary: A concession provides a more favorable outcome than the conflict that would follow defiance, but if Challenger knows that Defender will concede, Challenger will always attack and deterrence will always fail. Zagare and Kilgour (2000) label this dilemma the “paradox of mutual deterrence.” Classical deterrence theory offers two primary solutions.

The first proposed solution is for Defender to make an irrevocable commitment to a hard-line strategy. Such irrevocable commitments are made by burning bridges to limit one’s options by eliminating the ability to back down, even though that would be the preferred alternative (e.g., Kahn, 1962; Schelling, 1966). So Defender makes an irrevocable commitment to defy and must communicate this commitment to Challenger. Then Challenger is faced with the choice of remaining at the Status Quo by cooperating or defecting and starting a Conflict. Since choices of cooperate by Challenger and defy by Defender are mutual best responses, this strategy pair denotes a Nash equilibrium, with Status Quo as the outcome. The problem, however, is that if Challenger does attack, then Defender’s only rational response would be to concede, leading to Defender Concedes. Although the strategy pair (cooperate, defy) is a Nash equilibrium, it is not subgame perfect because it involves an irrational choice by Defender off the equilibrium path.6 The only subgame perfect equilibrium is the strategy pair (defect, concede), which results in Defender Concedes.

The second solution to this dilemma offered by classical deterrence theorists is threats that leave something to chance (Schelling, 1960). These threats allow Defender to circumvent the problem of irrational action by threatening to take action “that raises the risk that the situation will go out of control and escalate to a catastrophic nuclear exchange” (Powell, 2003, p. 90). Thus, rather than relying upon a threat to make an irrational choice for war, Defender can simply make a rational choice to raise the risk of war and leave the question of whether war starts or not to chance. Powell (1990, 2003) demonstrates that threats that leave something to chance not only lead to successful deterrence, but also result in a perfect equilibrium.

The idea of threats that leave something to chance rests upon the possibility of accidental war. There is a lot of speculation about this possibility (e.g., Schelling, 1966; Bracken, 1983; Blair, 1993), with the outbreak of World War I often cited as the prime example of an inadvertent war. However, close examination of the coming of World War I shows that it arose because leaders chose to go to war, not because they were accidentally drawn into it (e.g., Trachtenberg, 1991; Mulligan, 2010; Zagare, 2011).

Schelling suggests that in most crises, one side or another will be willing to run a greater risk of mutual assured destruction to achieve its goals. Therefore, credibility is determined by whose interests are more greatly threatened by an ongoing crisis and by who is more willing to take risks to protect their interests. Hence, deterrence becomes a “competition in risk taking,” as states employ brinksmanship in what the subtitle to Powell’s 1990 book calls “the search for credibility.” But a threat is said to be credible if it is believed (Schelling, 1966; George & Smoke, 1974; Jervis, 1985). Given that a nuclear attack invites one’s own destruction, the threat to choose to do so is not believable and thus is not credible. Schelling (1960) argues that while this is true, the threat to increase the risk of inadvertent war can in fact be believable. But since historical evidence shows that World War I—the prime example of accidental war—arose as a result of conscious decisions, not chance (Trachtenberg, 1991; Zagare, 2011), these threats that leave something to chance seem to be not credible after all.

Classical deterrence theory and its associated ideas, such as mutual assured destruction and brinksmanship, represent the conventional wisdom about deterrence. However, Zagare and Kilgour (2000) offer an alternative to classical deterrence theory, which they call “perfect deterrence theory.” Perfect deterrence theory was developed to overcome the logical deficiencies of classical deterrence theory. In particular, perfect deterrence theory departs from classical deterrence theory in its view of credibility. Zagare and Kilgour (2000) argue that threats are believable, and thus credible, when they are rational to carry out (also see Lebow, 1981; Betts, 1987; Smoke, 1987). Connecting credibility with rationality in this way is consistent with the treatment of credibility in game theory (e.g., Selten, 1975; Rasmusen, 1989).

This connection between credibility and rationality can be seen by reexamining the game in Figure 1. If Defender prefers Defender Concedes to Conflict, and Challenger knows this, Challenger has no reason whatsoever to believe that Defender will carry out its threat; thus, Defender’s threat is not credible. On the other hand, if Defender prefers Conflict to Defender Concedes, and Challenger knows this, Challenger would believe Defender’s threat (i.e., Defender’s threat would be credible). The simple deterrence game with a credible threat by Defender is shown in Figure 2.

Empirical Analyses of DeterrenceClick to view larger

Figure 2. Simple Deterrence Game with a Credible Threat.

In this game, Defender will choose to defy at node 2 because concession would result in her least preferred outcome. Knowing this, Challenger will cooperate at node 1 because the outcome that results (Status Quo) is preferred to the outcome that results from defection (Conflict). Thus, if Defender has a credible threat, Status Quo is the sole equilibrium outcome.

Accordingly, the solution to the paradox of mutual deterrence is the presence of credible threats (Zagare & Kilgour, 2000). When both sides possess credible and capable threats, Status Quo emerges as the rational outcome. Furthermore, the resulting equilibrium is subgame perfect, and it does not rest upon untenable assumptions of the possibility for accidental war.

This subtle yet significant switch forms the foundation of perfect deterrence theory. Zagare and Kilgour label their theory “perfect” because of their insistence on the use of perfect equilibria. This insistence stems from the observation that “perfectness rules out threats that are not credible” (Rasmusen, 1989, p. 87). However, Powell (1990, 2003) has also employed perfect equilibria, but his work certainly falls within classical, rather than perfect, deterrence theory. The real hallmark of perfect deterrence theory is the insistence that credibility varies, and that credibility is determined by a state’s preference between conflict and backing down.7

While classical deterrence theory is rooted in the basic assumption that the high costs of nuclear war make conflict the worst outcome for everyone, perfect deterrence theory is rooted in the assumption that different states have different preferences. While some may indeed prefer backing down to fighting, others prefer to fight, and only these latter states have credible threats. Although there are other differences between the two theories (Zagare, 2004; Quackenbush, 2011a; Quackenbush & Zagare, 2016), this one assumption makes a tremendous impact on the predictions and explanations offered.

The Divide Between Deterrence Theory and Empirical Analysis

This basic discussion of deterrence theory reveals several key areas where early empirical analyses were unable to test deterrence theory adequately. The case study literature was unable to test deterrence theory because these studies generally endeavored to criticize rather than test rational deterrence theory (e.g., George & Smoke, 1974; Steinbruner, 1976; Lebow, 1981, 1984; Jervis, 1982/1983; Jervis, Lebow, & Stein, 1985; Lebow & Stein, 1990). The quantitative literature on deterrence also has been limited by several factors.

First, with few exceptions (e.g., Weede, 1983, Huth & Russett, 1993), the early quantitative literature did not address the subject of general deterrence. Thus, it was unable to shed much light on the factors leading to the success or failure of general deterrence. Furthermore, because of the presence of selection effects, the findings on when deterrent threats work in immediate deterrence may be misleading. As Fearon (2002, p. 15) observes, “hypotheses that are valid for general deterrence should appear exactly reversed if we look at cases of immediate deterrence.”

Second, the early quantitative literature was not connected with deterrence theory. Most of the literature (particularly the Huth and Russett studies) was couched in terms of an expected-utility theory of deterrence. The potential challenger must consider whether to press its claim against the defender. Challenger has two options: either Back Down or Press Claim. If it presses the claim, Defender will either carry out the threat or not. The expected utility equations for Challenger’s two alternative courses of action are

EUBack Down=UBack Down

EUPress Claim=pCarry Out ThreatUThreat Carried Out+(1pCarry Out Threat)USuccessful Challenge

where UBack Down is the utility to Challenger for backing down; UThreat Carried Out is the utility if Defender carries out its threat; USuccessful Challenge is the utility if the challenge is successful (Defender does not carry out its threat); and pCarry Out Threat is the probability that Defender will carry out her threat. If EUPress Claim > EUBack Down, Challenger will press ahead and immediate deterrence fails. But if EUBack Down > EUPress Claim, Challenger will back down and immediate deterrence succeeds.

There are at least two serious limitations of this approach. First, the hypotheses tested have not been deduced. Rather, it has been inferred that factors such as relative power influence the expected-utility calculations. Second, and more important, such an expected-utility approach is unable to capture the strategic interactions between Challenger and Defender. Defender enters the model only through the probability that the threat is carried out. However, rational deterrence theory has moved beyond expected-utility models to game theoretic models, which enables theorists to capture the importance of strategic interaction between the challenger and defender.

In summary, an unfortunate divide exists between formal theories and the quantitative analysis of deterrence. There are several reasons for this disconnect: (a) while deterrence theory has typically focused on general deterrence, quantitative studies have focused almost exclusively on immediate deterrence; (b) quantitative studies generally have not tested rational deterrence theory, but rather have tested independently developed hypotheses; and (c) when studies have harkened back to rational deterrence theory, they have typically examined classical deterrence theory, a formal framework characterized by logical inconsistency and empirical inaccuracy.

Since rational deterrence theory is primarily expressed through game-theoretic models, empirical tests of the theory need to be able to test predictions that result from such models. Two primary avenues are available for such tests: evaluation of equilibrium predictions and evaluation of relationship predictions (Morton, 1999). Evaluation of equilibrium predictions entails comparison of the outcome predicted in equilibrium at each observation with the outcome actually observed.

Perfect deterrence theory consists of a variety of related game-theoretic models that account for the impact of credibility and capability on deterrence. The core of the theory includes models of unilateral deterrence (Zagare & Kilgour, 2000, ch. 5), mutual deterrence (Zagare & Kilgour, 2000, ch. 4), and extended deterrence (Zagare & Kilgour, 2000, chs. 6–9). Perfect deterrence theory provides a theory of general deterrence, so empirical analyses need to examine general deterrence in order to test it properly (Quackenbush, 2011b).

Modern Empirical Developments

Fortunately, the empirical analysis of deterrence has made important strides forward in recent years. This article reviews studies focused on five key areas: attempts to bridge the formal-quantitative divide in the study of deterrence; development of modern, theoretically driven case studies; the effect of alliances on deterrence; the relationship between reputations and credibility; and the effect of nuclear weapons on deterrence.

Bridging the Formal-Quantitative Divide

Quackenbush (2011b) attempts to bridge the gap between formal theories of deterrence and empirical research—discussed in the previous section—through several important steps. First, he argues that identifying opportunity for conflict is the key to selecting cases of general deterrence, and develops the concept of a politically active dyad in order to do so (Quackenbush, 2006a, 2011b). An empirical test demonstrates that this concept captures opportunity as a necessary condition for international conflict.

He then evaluates both equilibrium predictions and relationship predictions of perfect deterrence theory. Quackenbush (2010, 2011b) tests the equilibrium outcome predictions of perfect deterrence theory. Since the equilibrium predictions of perfect deterrence theory rely on the actors’ preferences, this requires explicit specification of utility functions for the actors involved. To do this, he uses relative power as a measure for probability of victory and measures utilities based on similarity of alliance portfolios. Quackenbush (2010, 2011b) uses binary and multinomial logit methods to examine the prediction of militarized interstate disputes and of particular game outcomes, and the results indicate that the predictions of perfect deterrence theory are generally supported by the empirical record.

Quackenbush (2011b, 2006b) also develops an extension of deterrence theory by introducing a formal model that considers direct and extended deterrence situations simultaneously. He develops the Three-Party Extended Deterrence Game and analyzes it in conditions of both complete and incomplete information. These analyses allow him to draw conclusions not only regarding extended deterrence, but also regarding the related areas of alliance reliability and war expansion.

Quackenbush (2011b) also applies perfect deterrence theory to the analysis of conflict settlements (see also Senese & Quackenbush, 2003). Different types of deterrence are required to maintain peace following a conflict, and because perfect deterrence theory shows that unilateral deterrence is more stable than mutual deterrence, he makes predictions about the stability of different types of conflict settlements. Further, these predictions are strongly supported by the empirical record. This is an insight that was not gained through other analyses of the same subject, and it provides a useful test of perfect deterrence theory’s relationship predictions.

A very different approach to bridging the formal-quantitative divide is taken by Signorino and Tarar (2006), who utilize a strategic probit model to produce a unified theory and test of extended immediate deterrence. Strategic probit provides a method for integrating the theoretical and empirical models, while accounting for nonmonotonic influences of independent variables resulting from strategic interaction. This is a promising avenue for future studies of deterrence.

Collectively, these efforts have gone a long way toward bridging the divide between formal theories and quantitative analyses of deterrence. Thus, they represent an important advance over earlier quantitative studies. The next set of developments has occurred in understanding particular cases, representing an important advance over the early case study literature on deterrence.

Understanding Particular Cases

Most attempts to test deterrence theory have utilized large-N, quantitative methods. Such analysis is useful because of the generalizable nature of conclusions derived from it. However, case studies are also useful, particularly when they are theoretically driven. Since quantitative analyses demonstrate that perfect deterrence theory is generally supported by the historical record (e.g., Quackenbush, 2010), there is evidence that the theory can be applied usefully to particular cases.

This can be done through the application of the insights of perfect deterrence theory to detailed case studies of particular historical episodes in order to understand these intrinsically interesting events more completely. For example, Quackenbush and Zagare (2006) have applied perfect deterrence theory to an analysis of the war in Kosovo to answer questions—such as why the threat of bombing from the North Atlantic Treaty Organization (NATO) was unable to deter Serbia, and why Serbia escalated ethnic cleansing later, once the bombing started—to which others have struggled to address.

In addition, Zagare (2011) explains the July 1914 crisis leading to World War I through an analytic narrative based on perfect deterrence theory. He does so by addressing a series of four questions. First, why did Germany and Austria ally in 1879 (Zagare, 2011; Zagare & Kilgour, 2003)? Applying the Tripartite Crisis Game of perfect deterrence theory, he shows that Germany chose to ally with Austria in order to prevent Austria from allying elsewhere. Second, he considers why Germany gave Austria-Hungary a blank check in 1914 (Zagare, 2009a, 2011). He uses the same model and shows that German behavior was consistent with equilibrium play, given Austria’s actions. The third question posed is: Why did Russia and France go to war (Zagare, 2009b, 2011)? To examine this question, Zagare applies the Asymmetric Escalation Game of perfect deterrence theory. Finally, Zagare (2011) addresses the question of why Britain entered the war (see also Zagare & Kilgour, 2006). He once again employs the Tripartite Crisis Game to explain Britain’s struggle with the deterrence versus restraint dilemma.

Zagare’s (2011) analysis demonstrates that perfect deterrence theory offers coherent explanations of the major questions regarding the outbreak of World War I. This provides not only an important test of perfect deterrence theory, but also a model for how to conduct theory-driven case studies. Furthermore, he shows that although general war was not sought by any of the actors, the war was no accident.

In a similar vein, Zagare (2016) applies perfect deterrence theory to provide a general explanation of the Cuban Missile Crisis. There has been a long history of attempts to use game-theoretic models to explain this crisis, but each has been incomplete or deficient (Zagare, 2014). In contrast, Zagare (2016) shows that one particular equilibrium of the Asymmetric Escalation Game of perfect deterrence theory is consistent with each of the key strategic aspects of the crisis: why the Soviets installed missiles in Cuba, why the American response was measured, and why the crisis ended in a compromise.

Alliances and Deterrence

The relationship between alliances and deterrence is another key focus in recent empirical analyses of deterrence. Alliances are particularly relevant for extended deterrence, which deals with a state’s attempt to deter another from attacking a third state. Thus, the goal of extended deterrence is to deter attacks on other states, and alliances are expected to be a key mechanism for shoring up the credibility of extended deterrence threats (Quackenbush, 2006b; Werner, 2000; Zagare & Kilgour, 2000). Leeds (2003) conducts a quantitative analysis of the effect of alliances on conflict and finds three important trends. First, target states that have defensive alliances are significantly less likely to be attacked than are other targets, indicating the deterrent effect of defensive alliances. The second and third findings relate to the challenger’s alliances. If the challenger has an offensive ally that calls for one or more additional states to join the attack against the target or has a relevant neutrality pact that calls for potential joiners to stay out of a conflict against the target, then conflict is significantly more likely to occur. Thus, alliances that work against the stability of deterrence are found to indeed undermine deterrence effectiveness.

Johnson and Leeds (2011) seek to build on the Leeds (2003) finding that defensive alliances have an important effect on deterrence by taking a closer look at defense pacts. They examine a much broader time frame and the possibility that defense pacts produce initiation or escalation effects that would increase the likelihood of international conflict. In their analysis, they find that “defense pacts are a useful tool for deterrence, and they do not have consistent side effects that undermine peace” (Johnson & Leeds, 2011, p. 62).

Benson (2011) adds to the literature on alliances and deterrence by distinguishing between deterrence alliances, which seek to prevent an adversary from doing something, and compellent alliances, which seek to get an adversary to stop doing something. He finds that only conditional deterrent alliances are able to deter conflict, and only when minor power protégés are allied with major power defenders. Other types of alliances, however, either do not affect the likelihood of deterrence success or actually increase the likelihood of conflict.

These studies not only reach important findings regarding the effect of alliances on deterrence, but also provide important examples of how modern quantitative methods can be used to examine the impact of key variables on deterrence.

Reputations and Credibility

Another important focus of recent developments in the study of deterrence has been on identifying credibility. Perfect deterrence theory demonstrates that credibility is an important determinant of deterrence success. In the presence of complete information, a state’s credibility is simply its preference between fighting and backing down; it either has a credible threat (i.e., prefers conflict) or does not (i.e., prefers backing down). However, states seldom possess such full information about their opponents.

When there is incomplete information and a state’s preference between fighting and backing down is not known to its opponent, the situation is more complicated. In this case, a state’s credibility is the opponent’s estimate of the probability that it prefers fighting to backing down; thus, credibility varies continuously between 0 and 1 (Zagare & Kilgour, 2000). Forming accurate estimates of the opponent’s credibility is complicated by the reality that states have incentives to misrepresent their private information (Fearon, 1995). Thus, states have incentives to claim that they prefer to fight rather than back down, regardless of their actual preference between the two. How can states credibly communicate their commitment to fight in the face of these difficulties?

Scholars seeking to answer this question have taken different approaches. Sartori (2005) develops a reputational theory of diplomacy whereby defenders acquire reputations for honesty or bluffing, depending on whether they carry through on their threats to defend against the challenger. This builds on a number of previous studies addressing the impact of reputations on deterrence (see Huth, 1997, for a review). Sartori (2005) finds that a defender’s reputation for honesty enhances their threat credibility and therefore increases the likelihood of successful deterrence; on the other hand, a reputation for bluffing undermines threat credibility.

In contrast, Press (2004, 2005) proposes a current calculus model, which evaluates credibility based on the balance of power and interests at stake, and argues that it does a better job of gauging states’ perceptions of their opponents’ credibility than the past actions model, which argues that credibility depends on one’s record for keeping or breaking commitments. His focus on assessing the interests at stake to determine credibility is quite reasonable, given that credibility deals with a state’s preference between backing down and conflict.

However, it is important to distinguish between credibility and capability; whereas capability is a necessary condition for deterrence success, credibility is not (Zagare & Kilgour, 2000). Assessments of the balance of power appear to have more to do with a state’s preference between conflict and the status quo than a state’s preference between conflict and backing down, so it appears that Press is conflating credibility and capability. For example, he argues that Britain’s threat to defend Poland in 1939 was not credible, in large part because Germany (especially Adolf Hitler) misjudged the balance of power. It seems clear that, although they could not be certain, Germany believed that British intervention was likely, and thus the British threat was credible. But as Weinberg (1995, p. 91) states, “in August 1939 Hitler preferred to attack Poland as a preliminary to attacking France and England, but he was quite willing to face war with the Western Powers earlier if that was their choice.” In other words, Germany preferred conflict with France and Britain to the status quo; despite being credible, the British threat was not capable.

A different approach to this issue is taken by Danilovic (2001b, 2002) in her quantitative studies of extended deterrence. She argues that a state’s inherent credibility—determined in large part by its regional interests—is a far more important predictor of deterrence outcomes than attempts to shore up credibility through the use of commitment strategies, as recommended by Schelling (1960, 1966) and other classical deterrence theorists.

Through her focus on credibility, Danilovic (2002) directly addresses a key distinction between perfect and classical deterrence theory. As discussed previously, the reason that classical deterrence theorists focus on commitment tactics as ways to shore up credibility is that they assume that all threats are inherently incredible. Zagare and Kilgour (2000), on the other hand, argue that states’ threats are credible only to the extent that the state actually prefers conflict to backing down. Accordingly, Danilovic’s analysis can be seen as an attempt to determine what factors (relative power, regional interests, and democracy) lead states to prefer conflict over backing down. Connecting Danilovic’s (2002) argument about inherent credibility to Zagare and Kilgour’s (2000) arguments about credibility reveals that Danilovic’s analysis provides a useful evaluation of perfect deterrence theory’s relationship predictions.

Nuclear Weapons

Deterrence theory came to prominence in academic and policy-making circles because of the threat of nuclear holocaust during the Cold War. Therefore, many scholars have focused on the dynamics of nuclear deterrence.8 Others have focused specifically on conventional deterrence (e.g., Mearsheimer, 1983; Shimshoni, 1988; Quester, 1986). Support for the analytical distinction between the two rests on the notion that “nuclear weapons dissuade states from going to war much more surely than conventional weapons do” (Waltz, 1988, p. 625).

Much of this early literature specifically on nuclear deterrence was theoretical in nature. Nonetheless, there have also been empirical examinations. In a fairly early quantitative study on the subject, Huth (1990) examines the impact of nuclear weapons on extended deterrence. He finds that possession of nuclear weapons by a defender increases the likelihood of deterrence success, but the effect is weaker than the immediate balance of conventional forces. In contrast, Geller (1990, p. 291) finds that nuclear weapons do not “impede escalatory dispute behavior by either nuclear or nonnuclear antagonists.”

More recent studies have continued to yield mixed results about the effect of nuclear weapons. Rauchhaus (2009) finds that nuclear weapons do not deter conflict below the threshold of war, although they do appear to make war less likely. This supports the idea of the stability-instability paradox first raised by Snyder (1961). Horowitz (2009) examines not only the effect of nuclear weapons on conflict, but how long states have had nuclear weapons. He finds that new nuclear powers are especially risky and thus conflict prone, although states appear to become less conflict prone as they gain nuclear weapons experience.

Other studies find nuclear weapons to be more stabilizing. Fuhrmann and Sechser (2014) find that alliance commitments from nuclear weapons states enhance the stability of extended deterrence, although stationing the weapons on the protégé’s territory does not seem to help. This, of course, raises the possibility that the result is being driven by the defender’s power status more generally, rather than possession of nuclear weapons per se. Beardsley and Asal (2009) find that opponents of nuclear weapons states are more constrained in their use of force. In contrast, Sechser and Fuhrmann (2017, p. 258) find overwhelming evidence that “nuclear weapons have sharp and significant limitations” in their effectiveness as instruments of coercion.

Overall, the empirical evidence regarding the effect of nuclear weapons on deterrence is mixed, despite the clear expectation of classical deterrence theorists that they are stabilizing. This should not be surprising because classical deterrence theorists’ claim that nuclear warfare entails such high costs that it is the worst possible outcome for all sides leads to logical problems. It is precisely the assumption that conflict is the worst possible outcome that leads to the paradox of mutual deterrence discussed previously. If conflict—nuclear or conventional—indeed is always the worst possible outcome, deterrence can never be successful. Any rational state that is attacked will always capitulate rather than bring about its own worst outcome, and knowing this, challengers will always attack.

The only logically consistent resolution to this paradox is the existence of mutually credible threats, where each state prefers to fight rather than back down (Zagare & Kilgour, 2000). Accordingly, if classical deterrence theory is correct that nuclear weapons make conflict the worst possible outcome—and thus, less preferable than backing down—then they are destabilizing, not stabilizing. If classical deterrence theory is not correct in this assumption, then the fundamental idea that deterrence is a game of Chicken falls apart. In any case, Zagare and Kilgour demonstrate that, beyond a certain threshold, the ability to impose additional costs has no effect on the stability of deterrence. Thus, as Morgan (2003, p. 133) argues, “nuclear deterrence … is given too much credit for the long peace.”


Many discussions of the study of deterrence focus on the development of deterrence theory. This is not surprising, as deterrence theory has comprised a major portion of the literature and produced many advancements in our understanding of deterrence. Nonetheless, there also have been many lively and important empirical studies of deterrence over the years.

This article has reviewed the empirical literature on deterrence. Early empirical studies of deterrence were highly limited for varying reasons. Much of the early case study literature did not seek to test deterrence theory. Early quantitative studies sought to do so, but they were hampered by rudimentary methods, poor research design, and/or a disconnect between quantitative studies and formal theories of deterrence.

Modern empirical studies of deterrence have made great strides forward in bridging the formal-quantitative divide in the study of deterrence and conducting theoretically driven case studies. Further, studies have explored the effect of specific variables on deterrence, such as alliances, reputations and credibility, and nuclear weapons. Future empirical studies of deterrence should build on these modern developments. In addition, they should further explore perfect deterrence theory, given its logical consistency and empirical support.


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(1.) In contrast, World War II consumed about 3 million tons of TNT in total (Rhodes, 1986, p. 563).

(2.) The Cuban Missile Crisis has often been considered a case of successful deterrence, resulting in a victory by the United States (e.g., Schelling, 1966; Snyder & Diesing, 1977). More modern evidence and explanations, however, show that the outcome of the crisis is more accurately considered a compromise (Zagare, 2014). In either case, war was avoided.

(3.) Levy (1988) and Huth (1999) provide reviews of the empirical literature on deterrence.

(4.) These are not the only two theories of deterrence. For example, Davis and Arquilla (1991a, 1991b) and Arquilla and Davis (1992) develop a separate theory of deterrence in a series of studies for RAND.

(5.) Schelling (1966) also introduced the distinction between compellence and deterrence. He argues that compellence—attempting to convince an opponent to stop an action that has already started—is more difficult than deterrence, which focuses on preventing an opponent from starting the action in the first place. Some scholars make an explicit distinction between the two, while others do not.

(6.) Nash equilibria require rational choices only along the equilibrium path, whereas subgame perfect equilibria require every possible decision to be rational. For a discussion of the distinction between the two equilibrium concepts, see Morrow (1994).

(7.) The analysis here assumes complete information, where each actor’s preferences are common knowledge. Zagare and Kilgour (2000) also examine situations of incomplete information, where each actor forms beliefs about its opponent’s preference between conflict and backing down. In that case, a state’s credibility results from its opponent’s belief about its type. While the details are different, the implications are quite similar.

(8.) For reviews of the literature on nuclear deterrence, see Harvey and James (1992) and Gartzke and Kroenig (2016).