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International Interactions, 36:60–85, 2010Copyright © Taylor & Francis Group, LLCISSN: 0305-0629 print/1547-7444 onlineDOI: 10.1080/03050620903554069

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GINI0305-06291547-7444International Interactions, Vol. 36, No. 1, Jan 2010: pp. 0–0International Interactions

General Deterrence and International Conflict: Testing Perfect Deterrence Theory

Testing Perfect Deterrence TheoryS. L. Quackenbush

STEPHEN L. QUACKENBUSHUniversity of Missouri

Since general deterrence necessarily precedes immediate deterrence,the analysis of general deterrence is more fundamental to anunderstanding of international conflict than is an analysis ofimmediate deterrence. Nonetheless, despite a few exceptions, thequantitative literature has ignored the subject of general deterrence,focusing almost exclusively on situations of immediate deterrence.My purpose in this essay is to fill this evidentiary gap by subjecting arecently developed theory of general deterrence—Perfect DeterrenceTheory—to a systematic test by examining general deterrence from1816–2000. The results indicate that the predictions of perfect deter-rence theory are strongly supported by the empirical record.

KEYWORDS conflict, deterrence, empirical testing of formalmodels, multinomial logit

Deterrence is the use of a threat (explicit or not) by one party in an attemptto convince another party not to upset the status quo. These threats havetwo purposes. The purpose of direct deterrence is to deter a direct attack onthe defender. The goal of extended deterrence, conversely, is to deter attackon one’s allies (Snyder 1961:276–277). In addition, Morgan (1983) identifiestwo basic kinds of deterrence situations: immediate and general. Immediatedeterrence “concerns the relationship between opposing states where atleast one side is seriously considering an attack while the other is mountinga threat of retaliation in order to prevent it” (Morgan 1983:30). Classic

A previous version of this paper was presented at the 2002 annual meeting of the Peace Science Society,Tucson, AZ. I would like to thank Frank Zagare, Paul Senese, Paul Hensel, Sara Mitchell, Pat James, andJerome Venteicher for helpful comments and suggestions.

Address correspondence to Stephen L. Quackenbush, Assistant Professor, Department ofPolitical Science, 113 Professional Building, University of Missouri, Columbia, MO 65211,USA. E-mail: [email protected]

Downloaded By: [Quackenbush, Stephen L.] At: 15:26 10 March 2010

Testing Perfect Deterrence Theory 61

examples include the July Crisis of 1914, the Cuban Missile Crisis of 1962and most, if not all, acute interstate crises. General deterrence, by contrast,“relates to opponents who maintain armed forces to regulate their relationshipeven though neither is anywhere near mounting an attack” (Morgan 1983:30).Thus, general deterrence has less to do with “crisis decisionmaking” thanwith everyday decisionmaking in conflictual or adversarial relationships.

Huth (1988) combines these two kinds of deterrence situations withthe two types of deterrent threats to form four categories of deterrence:direct-immediate deterrence, direct-general deterrence, extended-immediatedeterrence, and extended-general deterrence. Unlike many other works ondeterrence, this paper focuses on direct-general deterrence.

The need for immediate deterrence indicates that general deterrencehas previously failed (Danilovic 2001). If general deterrence succeeds, crisesand wars do not occur. Since general deterrence necessarily precedesimmediate deterrence, the analysis of general deterrence is more fundamentalto an understanding of international conflict than is an analysis of immediatedeterrence. Furthermore, because of selection effects, examining immediatedeterrence without consideration of general deterrence can lead to mislead-ing empirical results. As Fearon (2002:15) observes, “hypotheses that arevalid for general deterrence should appear exactly reversed if we look atcases of immediate deterrence.”

Unfortunately, a divide exists between formal theories and the empiri-cal analysis of deterrence. One reason for this divide is that while formaltheories have focused on general deterrence, the quantitative literature hasfocused almost exclusively on immediate deterrence (Huth 1999). Importantexceptions include Weede (1983), who examined extended deterrence inthe cold war, and Sorokin (1994), who examined the impact of alliance for-mation on extended general deterrence within the Arab–Israeli conflict.Given their focus on extended deterrence, these studies are unable to pro-vide insight on direct general deterrence. Huth and Russett (1993) didexamine direct general deterrence within the context of enduring rivalries.They find that the balance of forces, arms races, and domestic conflict areall important determinants of deterrence outcomes. However, they do notdirectly test any specific theory of deterrence; indeed, formal theories ofgeneral deterrence have never been subjected to direct empirical testing.

Indeed, this problem has unfortunately plagued formal theories through-out political science (Green and Shapiro 1994), not only in the study ofdeterrence. This is unfortunate since deterrence theory appears to shedgreat light on the dynamics of deterrence, yet without extensive empiricalanalysis, one cannot know how well these theories explain real-world phe-nomena. One reason for this lack of testing is that, while selection of imme-diate deterrence cases has received a great deal of attention (for example,Huth and Russett 1984, 1988, 1990; Huth 1988), criteria for the selection ofgeneral deterrence cases have remained elusive.


62 S. L. Quackenbush

This paper has two related purposes. The specific purpose is to fill thisevidentiary gap by subjecting perfect deterrence theory—a recently devel-oped theory of general deterrence—to a systematic test. I do so for severalreasons. First, perfect deterrence theory (Zagare and Kilgour 2000) is sup-ported by a formal logic with explicit theoretical expectations that facilitatesempirical testing. Second, several preliminary tests of perfect deterrencetheory have rendered promising, albeit provisional results (Senese andQuackenbush 2003; Quackenbush and Zagare 2006).1 And finally, as Huth(1999) points out, standard formulations of deterrence—to the extent thatthey have been explored empirically—are without compelling support.

The more general purpose is to develop the conceptualization and pro-cedures to make such a test possible. This is necessary to bridge the dividebetween formal theories and quantitative analyses of deterrence. Key con-ceptualizations include case selection for direct general deterrence—I arguethat identifying opportunity for conflict is the key. In addition, this paperoffers the first direct test of incomplete information equilibrium predictionsmade by formal deterrence theory. Conducting such a test requires mea-surement of the utilities the actors have for the different outcomes that mayemerge, so a modification of the measurement procedures developed byBueno de Mesquita and Lalman (1992) is used. Also, since incomplete infor-mation equilibria depend on each state’s estimate of the opponent’s credi-bility, a nonlinear transformation technique is developed to estimate thecredibility parameters.

To test perfect deterrence theory, I examine general deterrence from1816–2000. After detailing the equilibrium predictions of perfect deterrencetheory’s unilateral deterrence game, I more fully discuss the research designused to test them, including case selection, measurement of variables, andstatistical method. In the next section, I discuss the empirical results and thetheory’s ability to explain general deterrence and international conflict. Theresults indicate that perfect deterrence theory is well supported by theempirical record. Finally, I compare these findings to previous results sup-porting Bueno de Mesquita and Lalman’s (1992) international interactiongame that is the basis of one of the most influential and important theoriesof interstate conflict.

UNILATERAL DETERRENCE GAME

Perfect deterrence theory is an axiomatically distinct theoretical alternativeto classical deterrence theory, which focuses on ideas such as brinkmanshipand mutual assured destruction (for example, Schelling 1960, 1966; Powell

1In addition, Danilovic’s (2002) empirical findings are consistent with the theory.



1990; see Zagare 2004 for a summary of differences between the two). Ifocus on testing equilibrium predictions of the Unilateral Deterrence Gamedeveloped by Zagare and Kilgour (2000: chapter 5).2 Furthermore, unlikemost previous tests of game-theoretic models, I focus on incomplete infor-mation conditions, since incomplete information is an important factor lead-ing to war (Fearon 1995).

Figure 1 shows the structure of this game, which has two players,Challenger and Defender. At node 1, Challenger can choose whether tocooperate or defect: if he cooperates, the Status Quo remains unchanged; ifhe defects, Defender has an opportunity to respond. At node 2, Defendercan choose whether to concede or defy. If she concedes, the outcome isDefender Concedes (DC), but if she defies, the next choice is Challenger’s.At node 3, Challenger can choose to concede, resulting in ChallengerDefeated (CD), or defy, resulting in Conflict (DD).

Challenger’s utilities for outcome x are cx, whereas Defender’s utilitiesare dx, as indicated in Figure 1. Perfect deterrence theory highlights the

2Perfect deterrence theory relies on three core models: the Unilateral Deterrence Game, the GeneralizedMutual Deterrence Game, and the Asymmetric Escalation Game (Zagare and Kilgour 2000). The lattergame focuses on situations of extended deterrence, and is therefore inappropriate for the current focuson direct deterrence. Furthermore, the unilateral deterrence game, unlike the mutual deterrence game,allows for differentiation between states within a dyadic relationship. Accordingly, I focus on testingequilibrium predictions of the Unilateral Deterrence Game

FIGURE 1 Unilateral deterrence game. Challenger defects initially with probability x. Defenderdefies with probability y.

Challenger

Defender

Challenger

Status Quo cSQ, dSQ

Defender Concedes

cDC, dDC

Challenger Defeated

cCD, dCD

Concede

Cooperate 1 – x

Concede 1 – y

Defy

Defy y

Defect x

Node 1

Node 2

Node 3

Conflict cDD, dDD



importance of two variables: capability and credibility. A state’s threat iscapable if the threatened party believes that it would be worse off if thethreat were carried out than if it were not. For example, if Defender has acapable threat, then Challenger prefers Status Quo to Conflict.

Credible threats are believable, and in order to be believable, they mustbe rational to carry out (Zagare 1990). Therefore, a state that prefers conflictto backing down has a credible threat, and is said to be “Hard.” On theother hand, a state that would rather back down than fight has an incrediblethreat, and is said to be “Soft.”

EQUILIBRIUM PREDICTIONS

Zagare and Kilgour (2000) provide complete solutions and discussion of theUnilateral Deterrence Game. The equilibria are presented briefly in theappendix, as is an original analysis of the situation where Defender’s threatis not capable. These equilibria are the basic predictions of perfect deterrencetheory to be tested. However, one cannot observe directly what equilibriumis present at any one time; only the outcome can be observed. Therefore,the equilibria must be further explicated to generate specific outcome pre-dictions for the wide variety of conditions that may exist in reality. Threesituations may arise, each generating different predictions.

The first condition that may exist is where Challenger prefers the StatusQuo to Defender Concedes. Given no incentive to defect, Challenger willalways cooperate, leading to the Status Quo. Secondly, if Challenger prefersConflict to the Status Quo, then Defender lacks a capable threat. The solutionpresented in the appendix shows that in this case the outcome is Conflict ifDefender is Hard, and if Defender is Soft the outcome is Defender Concedes.

Lastly, the most complicated scenario is when Challenger prefersDefender Concedes to Status Quo and Defender has a capable threat. In thiscase, only Certain Deterrence Equilibria make a unique outcome prediction(Status Quo) over their entire range of existence. Multiple outcomes emergeat intermediate (Separating Equilibrium) and low (Bluff and Attack Equilibria)levels of Defender credibility.

Under a Separating Equilibrium, the player choices are completelydetermined by their type. Therefore, Hard Challengers always defect atnode 1. A Hard Defender also always defies, so if both players are Hard, theoutcome is Conflict. However, a Soft Defender always concedes, so the out-come (with a Hard Challenger) is Defender Concedes. But if Challenger isSoft, he will always cooperate, resulting in Status Quo.

With an Attack Equilibrium, Challenger always defects initially, regard-less of type. Therefore, the outcome reached is largely determined byDefender’s type. If Defender is Hard, she will defy and the outcome is Conflictif Challenger is Hard as well. But in the unlikely event that a Soft Challenger



faces a Hard Defender, then the outcome is Challenger Defeated. A SoftDefender always concedes, so the outcome is Defender Concedes.

Unfortunately, the Bluff Equilibrium does not provide unique outcomepredictions for each pair of player types like the other equilibria do. A HardChallenger always defects, as does a Hard Defender. Therefore, Conflictresults if both players are Hard. However, a Soft Defender defies with somepositive probability, so the outcome (with a Hard Challenger) will be eitherDefender Concedes (if Defender concedes) or Conflict (if Defender defies).A Soft Challenger also defects with some positive probability. So if a SoftChallenger faces a Hard Defender, the outcome will be either Status Quo (ifChallenger cooperates) or Challenger Defeated (if Challenger defects ini-tially). If both players are Soft almost anything can happen. If Challengerdefects initially and Defender concedes, the outcome is Defender Concedes.But if Defender surprises Challenger by defying at node 2, then the out-come is Challenger Defeated.3 Finally, if Challenger cooperates, the out-come is Status Quo.

One additional equilibrium—Steadfast Deterrence Equilibrium—exists.As with the Certain Deterrence Equilibrium, Status Quo is the only possibleoutcome. However, this equilibrium exists at intermediate and low values ofDefender credibility, and thus coexists with equilibria of other types. Therefore,through the Steadfast Deterrence Equilibrium, perfect deterrence theory pre-dicts that the Status Quo is always possible as long as Defender’s threat iscapable. Thus, Zagare and Kilgour’s (2000:149) claim that successful “deter-rence could conceivably emerge under (almost) any conditions in a one-sideddeterrence relationship.”

These three basic conditions—1) where Challenger prefers Status Quo toDefender Concedes, 2) where Defender lacks a capable threat, and 3) whereDefender’s threat is capable—cover the entire range of possibilities. The out-come predictions for each scenario are summarized in Table 1 and serve asthe equilibrium predictions to be tested in the empirical analysis to follow.

RESEARCH DESIGN

With the equilibrium outcome predictions now made, I turn to a presentationof the research design used to test these predictions. I will discuss the selec-tion of cases, measurement of the dependent and independent variables,and the statistical method used in turn. The lack of quantitative testing offormal deterrence theory has been driven in large part by the difficultiespresented by these issues. These conceptualizations are crucial not only forthe specific task of testing perfect deterrence theory but also the more

3Since Challenger is Soft, he will always concede at node 3.



general task of making such tests possible and thereby somewhat bridgingthe divide between formal theories and quantitative analysis of deterrence.

Case Selection

Case selection has been the biggest obstacle to the empirical analysis ofgeneral deterrence (Huth 1999). The only previous quantitative study focus-ing on direct general deterrence is by Huth and Russett (1993:63, emphasisadded), who argue that “the population of enduring rivalries in the interna-tional system includes all dyadic relations in which a dispute created thepossibility of one or both parties resorting to overt military force to achievea gain or redress a grievance.” According to this line of reasoning, then,enduring rivalries are the proper cases for the study of general deterrence.Similarly, Diehl and Goertz focus attention on rivalries, whether or not theybecome enduring, and argue that “the rivalry approach provides a solution”(Diehl and Goertz 2000:91) to problems with deterrence case selection.

According to Diehl and Goertz (2000), a dyad is in a rivalry if theyengage in a militarized interstate dispute. Thus, selecting all rivalries ascases of general deterrence would capture (by definition) all failures of

TABLE 1 Equilibrium Outcome Predictions for the Unilateral Deterrence Game with Incom-plete Information

Existence conditionsRestrictions on

challengerRestrictions on defender Predicted outcome

1) cSQ > cDC – – Status Quo

2) cDD > cSQ– dDD > dDC Conflict– dDC > dDD Defender Concedes

3) cDC > cSQ and cSQ > cDD

Certain Deterrence EquilibriumpDef ³ ct – – Status Quo

Separating Equilibrium

cDD > cCDdDD > dDC Status Quo, Conflict

cs £ pDef £ ct dDC > dDD Status Quo, Defender ConcedescCD > cDD – Status Quo

Bluff Equilibrium

cDD > cCDdDD > dDC Status Quo, Conflict

pDef < cs and pCh £ dn

dDC > dDD Status Quo, Defender Concedes, Conflict

cCD > cDDdDD > dDC Status Quo, Challenger DefeateddDC > dDD Status Quo, Defender Concedes,

Challenger DefeatedAttack Equilibrium

pDef < cs and pCh ³ dncDD > cCD dDD > dDC

Status Quo, ConflictcCD > cDD Status Quo, Challenger Defeated

– dDC > dDD Status Quo, Defender Concedes

Note: For definitions of threshold parameters ct, cs, and dn, see the appendix.



general deterrence.4 However, deterrence in dyads that have not foughtwould be ignored, which is particularly problematic because those are thedyads where deterrence has always worked. Furthermore, identification ofthe length of a rivalry, and thus the span of general deterrence, requires theassumption that the rivalry begins either with the first dispute (and thusdeterrence failed when it was attempted for the first time), or at some arbi-trary length of time before the first dispute and after the last.5

Therefore, the rivalry approach is limited as a path to general deterrencecase selection. However, one can safely assume that every state wishes todeter attacks against itself—this is the basic rationale for the maintenance ofarmed forces (Morgan 1983). This assumption is equivalent to the allianceportfolio literature’s assumption that every state has a defense pact with itself(Bueno de Mesquita 1975; Signorino and Ritter 1999).6 Hence, the difficultpart of general deterrence case selection is not determining who makes deter-rent threats (everyone does), but rather what states the threats are directedagainst. General deterrent threats are directed against any state that mightconsider an attack; these are states that have the opportunity for conflict.

Thus, the key to selecting cases of general deterrence is identifyingopportunity for conflict.7 To identify cases where opportunity exists, Iuse the recently developed concept of politically active dyads (Quacken-bush 2006a). A dyad is politically active “if at least one of the followingcharacteristics applies: the members of the dyad are contiguous, eitherdirectly or through a colony, one of the dyad members is a globalpower, one of the dyad members is a regional power in the region ofthe other, one of the dyad members is allied to a state that is contiguousto the other, one of the dyad members is allied to a global power that isin a dispute with the other, or one of the dyad members is allied to aregional power (in the region of the other) that is in a dispute with theother” (Quackenbush 2006a:43). Quackenbush (2006a) finds that politi-cally active dyads are able to identify opportunity as a necessary condi-tion for international conflict, while previous measures of opportunity

4This is, of course, classifying militarized interstate disputes as general deterrence failures.5This length of time could be assumed to be 10 years, for example. Thus, if two states last disputed in1900, then the rivalry would continue to 1910. But if general deterrence is needed in 1910, why is it notneeded in 1911 as well?6In other words, every state threatens to respond if attacked, even though it may not actually carry outthe threat if attacked (just as defense pacts are not always honored when tested).7Thus, I argue that even “friendly” dyads, such as the United States and Canada, use general deterrenceto regulate their relationship. Each has an incentive to prevent the other from challenging the status quo;indeed, deterrence has failed between the United States and Canada six times since 1974. Furthermore,since identifying opportunity for conflict is the key to general deterrence case selection, some may con-clude that any study that uses politically relevant dyads (or politically active dyads) is an examination ofgeneral deterrence. While there is some merit to that view, most studies of international conflict do nothave the same focus on the credibility and capability of threats that deterrence theory does, so such ablanket statement is not necessarily valid.



such as politically relevant dyads and regional dyads are unable to doso. Thus, we can have confidence that all politically active dyads couldfight if they had the willingness to do so. The goal of deterrence is todissuade other states from attacking the deterring state. In other words,states seek to ensure that other states—those with the opportunity toattack—do not gain the willingness to attack, and they do this throughdeterrence. While other empirically verified causes of war certainlyimpact deterrence outcomes, opportunity is the key to general deter-rence case selection.

Some readers might be concerned that there is no attempt to determinewhether the challenger actually intends to attack, and thus, whether the lackof an attack can meaningfully be considered general deterrence success.This issue does not actually pose a problem for the analysis here. The pre-dictions being tested, from Table 1, are about particular game outcomes, nota dichotomous measure of deterrence “success” and “failure.” Furthermore,these predictions explicitly cover the case where the challenger has abso-lutely no interest in attacking. While the three non-status quo outcomes areessentially different categories of general deterrence failure, the status quooutcome is not necessarily the result of successful deterrence. For example,if Challenger prefers Status Quo to Defender Concedes, the only rationaloutcome is Status Quo. Although Challenger’s decision to not challenge thestatus quo in this case is not really “successful deterrence,” it is predicted byperfect deterrence theory.

For the cases that are selected (because they are politically active), Iemploy a directed-dyad-year unit of analysis. Within a directed dyad, thedirection of interaction is important; for example, United States→Japan isone directed dyad and Japan→United States is another. The UnilateralDeterrence Game theoretically differentiates between the roles played byeach state in a dyad, so employing directed-dyads enables empirical differ-entiation between the states in a dyad as well. Furthermore, since each statein a politically active dyad has the opportunity for conflict with the other,each state has an opportunity to challenge the status quo. Therefore, eachstate is considered to be a potential challenger. For example, in the UnitedStates→Japan directed dyad, the United States is Challenger and Japan isDefender, while in the Japan→United States directed dyad, Japan is Chal-lenger and the United States is Defender.

Because most international relations data are based on annualobservations, the year is the time period used for the cross-sectionaltime series data analysis conducted here. Therefore, each politicallyactive directed-dyad-year constitutes an observation. Since general deter-rence deals with the outbreak, rather than the continuation, of interna-tional conflict, I eliminate dyad-years marked by a conflict continuingfrom the previous year as well as ‘joiner’ dyads. Furthermore, I drop thedirected dyad B→A in years with a continuing conflict in the directed



dyad A→B.8 This results in a total of 384,865 politically active directed-dyad-years for the time period 1816–2000.9

Dependent Variable

The dependent variable for this analysis codes which outcome—Status Quo,Defender Concedes, Conflict, or Challenger Defeated—of the Unilateral Deter-rence Game occurred for each observation. These game outcomes aredetermined by using version 3 of the militarized interstate dispute (MID)data set (Ghosn, Palmer, and Bremer 2004). If no dispute was initiated for agiven directed dyad year, the deterrence outcome is coded as Status Quo.

The coding of the other deterrence outcomes is not as straightforward,but it is possible by utilizing information from both the outcome and thehostility level of the MID data set. The outcome variable of the MID datacategorizes whether the outcome of a dispute is victory, yield, stalemate,compromise, released, unclear, or joins ongoing war. More information isneeded, however, in order to capture the deterrence outcome rather thanjust the dispute outcome. This additional information is provided by thehostility level of each state in a MID, which is coded using a five-pointscale. The hostility level indicates whether no militarized action was takenby that state, a threat to use force was made, a display of force, an actualuse of force, or war.

Dispute initiation is equated to Challenger’s defection at node 1 of theunilateral deterrence game. However, to determine what outcome—DefenderConcedes, Challenger Defeated, or Conflict—is reached following Challenger’sinitial defection, it must be determined which player, if any, conceded. Unfor-tunately, the MID data do not indicate the sequence of events within a dis-pute. Nonetheless, the outcome and the hostility level variables can be usedto determine what game outcome best corresponds to each dispute.

If both sides use force, or the outcome is “joins ongoing war,” thegame outcome is coded Conflict. If mutual use of force did not occur, thena “victory by A” or “yield by B” is coded as Defender Concedes, whereas a“victory by B,” a “yield by A,” or a “released” outcome is coded as Chal-lenger Defeated.10 If there was no mutual use of force and the outcome was“unclear,” “stalemate,” or “compromise,” then I compare hostility levels todetermine the outcome.

8For detailed discussions of directed-dyads and joiners, see Bennett and Stam (2000c).9Because of missing data, the number of observations actually used in the analyses is reduced further.EUGene, version 3.1 (Bennett and Stam 2000a) was used to construct the data set.10The released outcome is “identified whenever the seizure of material or personnel culminates withtheir release from captivity” (Jones, Bremer, and Singer 1996:180). In game terms, Challenger backeddown in the end. Analyses (not reported here) reveal no significant differences between droppingreleased cases or including them.



If one state escalates to a higher hostility level than the other, it is rea-sonable to infer that the other state has conceded at some point rather thanto defy by continuing to escalate.11 Thus, if Defender’s highest hostility levelis lower than Challenger’s, then the outcome is Defender Concedes. But ifDefender escalates to a higher hostility level, the outcome is ChallengerDefeated. Finally, if both states escalate to the same hostility level, the outcomeis coded Conflict.

Variables for the individual outcomes are combined into a single cate-gorical variable. The resulting variable, called game outcome, is the dependentvariable for the analyses to follow.

Independent Variables

In order to test the predictions summarized in Table 1 for each observation,player types and credibilities must be measured. This requires measurementof the utility that each player has for the various outcomes in each dyadyear, a quite difficult task. Indeed, it has never been done with respect todeterrence theory.

The utilities for each outcome of a deterrence situation can be specifiedin terms of the costs and benefits of that outcome. For the two outcomesfollowing a concession—Defender Concedes and Challenger Defeated—theutility comes from the size of concession and the cost associated with thatoutcome.12 The utility for Conflict is a lottery between receiving one’sdemand and conceding the stakes to the other player, weighted by theprobability of victory.13

Following this logic, each player’s utility for each outcome can beexpressed in mathematical form. Accordingly, Challenger’s utility for eachoutcome is operationalized as

11Similar game outcome coding procedures have been employed by Bueno de Mesquita and Lalman(1992) and Bennett and Stam (2000b).12Following Bueno de Mesquita and Lalman (1992:43), I assume that the cost of conceding “after absorb-ing a first-strike blow is larger, the greater the power of the rival:” gx(1 – px).13I assume that domestic costs (fxpx) rise with the subjective probability of victory, since “the morepowerful participant in a dyadic relationship bears a greater burden for finding a peaceful resolution ofdifferences. Domestic populations are assumed to dislike bullying and to punish those who employ vio-lence if their power should have made them persuasive enough to resolve their disputes without it”(Bueno de Mesquita and Lalman 1992:46).

cSQ cu SQ= ( ) (1)

cDC c c c cu p= −( )Δ f (2)



and Defender’s utilities are operationalized similarly, where Δx is the size ofthe demand made by state x, px is the probability x wins, fx is the domesticpolitical cost associated with the use of force by x, gx is the cost borne by xupon giving in, and wx is the cost borne by x in a conflict.14

Bueno de Mesquita (1975) developed a technique to measure state’sutilities based on their portfolios of alliance commitments. This techniquehas been refined over time, and the procedures outlined by Bueno de Mesquitaand Lalman (1992: appendix 1) serve as the baseline for the measurement ofthe individual components of equations 1 through 4 used here. States’ utili-ties are measured using the similarity of foreign policy portfolios and riskattitudes (Bueno de Mesquita 1985). The probabilities of victory are esti-mated using relative power and estimates of the likelihood of interventionby third parties.15 In addition, several important changes have been made totheir procedures; details of these changes are provided in the appendix,along with an explanation of the nonlinear method developed to measureeach state’s credibility parameter.

Once the utilities, credibility parameters (pDef and pCh), and thresholdvalues (ct, cs, and dn) are measured, the equilibrium outcome predictionsfor each politically active directed dyad-year are made according to the cri-teria specified in Table 1. This results in four dummy variables: predictedStatus Quo, predicted Defender Concedes, predicted Challenger Defeated,and predicted Conflict. Each of these variables equals 1 if the correspondingoutcome is predicted in equilibrium for the current observation, and 0otherwise.

Since not all of the outcome predictions in Table 1 are unique, thesevariables are not mutually exclusive. That is, a value of “1” for predictedStatus Quo does not indicate that each of the other variables equals “0.” Forthose observations where multiple outcomes are predicted in equilibrium,the variable for each predicted outcome takes the value “1.” Therefore, eachof these four variables will be included in the multinomial logit models;

14These utilities for the various outcomes are equivalent to the utilities of some of the outcomes specifiedby Bueno de Mesquita and Lalman (1992). Specifically, cSQ = UA(SQ), cDC = UA(CapB), cCD = UA(CapA),and cDD = UA(WarA). The only exception is that no distinction is made here between the costs borne bythe attacker and target in a conflict—they are assumed to be equal (w). Although Bueno de Mesquita andLalman distinguished between the two cost terms theoretically, in their empirical testing the cost termswere assumed to be the same (a = t).15Complete details of the measurement procedures are provided by Bueno de Mesquita and Lalman(1992), as well as Bennett and Stam (2000a; 2005), who provide useful clarifications. I use the utilitycomponents drawn directly from Bennett and Stam’s EUGene software.

cCD c d c cu p= − −[ ( )]Δ g 1 (3)

cDD c c c c c c c c c d c c c cp u p p p u p p= − − − + − − − −[ ( ( ))] ( ) [ ( ( ))]Δ Δf w f w1 1 1 (4)



together, they serve as the primary independent variables for the predictionof game outcomes.

CONTROLS

These independent variables constitute the equilibrium outcome predictionsof perfect deterrence theory. However, a number of alternative explanationsof international behavior exist. Therefore, several control variables, repre-senting the major foci of recent conflict studies, are used to test the robust-ness of the results obtained. Some of these variables (particularly relativepower and S score) are components of the utility functions that form thebasis of the equilibrium predictions to be tested. However, it is possible thatthese variables exert an independent influence on deterrence outcomes inaddition to their influence on equilibrium predictions. Furthermore, sincethese individual components are combined in a different, nonlinear fashionwithin the unilateral deterrence game to generate equilibrium predictions,multicollinearity between the equilibrium predictions and the control vari-ables is not present.16

BALANCE OF FORCES

There is little dispute that relative power has an important effect on interna-tional conflict behavior. Most significantly, its importance has been high-lighted in previous empirical studies of deterrence (for example, Huth 1988).It is therefore important to control for the effect of the balance of forces inthe present analysis. I use the composite indicator of national capabilitiesfrom the Correlates of War project (Singer, Bremer, and Stuckey 1972) tomeasure military capabilities for each state. To determine the balance offorces in a dyad, I create a ratio of Challenger’s capabilities to the total capa-bilities of the dyad. The final variable, balance of forces, ranges from 0(when Challenger is weak compared to Defender) to 1 (when Challenger isvery strong compared to Defender).

S SCORE

Signorino and Ritter’s (1999) S score measures the similarity of foreign policypositions between states. Although S is an important component of themeasurement of utilities employed here, it is possible that similarity in foreignpolicy positions has an independent effect on the outcome of internationalinteractions. Therefore, I include it as a separate variable, which ranges

16Correlation between outcome predictions and control variables ranges from 0.002 to 0.25.



from –1 to 1, with positive values indicating increasingly similar allianceportfolios and negative values representing increasingly dissimilar portfolios.

DISTANCE

Geographic proximity has repeatedly been found (for example, Bremer1992) to be an important predictor of international conflict. To control forthe effects of proximity, the distance between states in a dyad is measured.I take the natural logarithm of the distance between capital cities, except forthe USSR and United States when other cities are included, and states withland borders are considered to be zero miles apart (Bennett and Stam2000a).

DEMOCRACY

The democratic peace literature (for example, Russett and Oneal 2001) hasrepeatedly found that democracies have seldom if ever fought one another.Furthermore, Schultz (2001) has found that democracy has an importanteffect on credibility. It is therefore important to control for the effect of jointdemocracy on deterrence outcomes. To measure democracy, I use the polity2 variable, which ranges from −10 to 10, of the Polity IV data (Marshall andJaggers 2002). I use the minimum democracy score for the dyad as a variablein the empirical analyses.

PEACE YEARS SPLINE

The final control variable is of more a methodological than substantive char-acter. Beck, Katz, and Tucker (1998) have argued that it is important forstudies of conflict using pooled dyadic time series to account for timedependence within dyads. In other words, while the standard statisticalassumption is that each observation is independent, observations of differentyears of the same dyad are not truly independent. I account for time depen-dence by employing Beck, Katz, and Tucker’s method of including peaceyears and three cubic spline variables that account for time dependence.

Statistical Method: Multinomial Logit

Because the dependent variable, game outcome, has more than two unor-dered categories, the appropriate statistical method to use is multinomiallogit. Since there are four categories, three equations are estimated. Theseequations independently estimate the effects of the independent variableson producing outcomes Defender Concedes, Challenger Defeated, and Conflictrelative to the Status Quo.



Two alternative models are available for empirical analysis of the multi-ple, unordered categories of the dependent variable employed here. Thefirst of these is strategic probit, which Signorino and Tarar (2006) utilized fora unified theory and test of extended immediate deterrence. Strategic probitprovides a method for integrating the theoretical and empirical models,while accounting for nonmonotonic influences of independent variablesresulting from strategic interaction (Signorino 1999, 2003). Thus, strategicprobit would provide an excellent avenue for empirically determining theimpact of factors such as balance of forces, arms races, and domestic conflicton general deterrence. However, since strategic probit uses a different solu-tion concept (quantal response equilibrium vs. perfect Bayesian equilibrium)and different information conditions (complete vs. incomplete information)than perfect deterrence theory, an empirical analysis using strategic probitwould not be a test of perfect deterrence theory’s equilibrium predictions,which is the purpose of this paper.

The second alternative would be a nested logit model. Nested logitmodels are models of a decision process that is made in stages in which thedecisions at later stages are limited by those made in earlier stages. Thisseems to fit nicely with the game structure examined here, where eachnode of the Unilateral Deterrence Game would correspond to a differentstage of the nested logit model. Unfortunately, nested logit is also notappropriate here, for two primary reasons. First, as with the strategic probit,it would not provide a test of the equilibrium predictions of perfect deter-rence theory. Secondly, nested logit models are unable to account for strate-gic interaction between multiple decisionmakers, and are thus onlyappropriate for analyses of a single decisionmaker’s nested decisions(Signorino 2003).

While the multinomial logit model is also a decision model that doesnot account for strategic interaction, that does not pose a problem for thisanalysis. Strategic interaction between Challenger and Defender is takeninto account through perfect deterrence theory, which makes equilibriumoutcome predictions prior to the empirical analysis. Thus, the theory isthe “decisionmaker” (deciding which outcome(s) is predicted for eachobservation), and the purpose of this analysis is to test how well the theorymakes those decisions.

RESULTS

I begin testing the equilibrium predictions of perfect deterrence theory out-lined in Table 1 through a base model—incorporating only the four outcomeprediction variables and the peace years spline variables—shown in Table 2.This model fits the data significantly better than a model including only theconstant term.



Beginning with predicted Status Quo, one can see that the coefficientfor this variable is insignificant for all but the Conflict equation. This indi-cates that predicting the status quo has no significant impact on the occur-rence of Defender Concedes or Challenger Defeated, while it increases theprobability of Conflict. This latter result is quite surprising; if robust, thisfinding would be problematic for the theory.

The impact of each of the non-status quo outcome predictions on theoccurrence of game outcomes is in line with expectations. The prediction ofDefender Concedes makes Defender Concedes significantly more likely tooccur, and significantly increases the probability of Challenger Defeated andConflict. Similarly, predicted Challenger Defeated makes all non-status quooutcomes, most importantly Challenger Defeated, more likely to occur. Theprediction of Conflict also has a significant impact in each equation. Inother words, if Conflict is predicted, all non-status quo outcomes (mostimportantly, Conflict) are more likely to occur.

To examine the robustness of these results against alternative explanations,the full multinomial logit model was run including the control variables. Thefull model, shown in Table 3, produces a highly significant fit to the data.The results of the full model indicate that the predictions of perfect deter-rence theory are quite robust.

Unlike the base model, predicted Status Quo is found to reduce theprobability of any non-status quo outcome, although the coefficient for theChallenger Defeated equation is not significant. Thus, although the resultsfor this variable were somewhat contrary to expectations in the base model,after other factors are controlled for the expected pattern emerges.

TABLE 2 Multinomial Logit Results without Control Variables

Outcome

VariableDefender Concedes

ChallengerDefeated Conflict

Predicted Status Quo b 0.0371 0.0584 0.3408*Seb 0.1295 0.2065 0.1655

Predicted Defender Concedes 0.6166*** 0.4580* 0.5387***0.1039 0.1806 0.1167

Predicted Challenger Defeated 1.3437*** 1.3298*** 1.4941***0.2216 0.2581 0.2118

Predicted Conflict 0.5470*** 0.8941*** 0.4696*0.1182 0.2013 0.1951

Constant −4.8726*** −6.4350*** −5.1042***0.1624 0.2565 0.1864

c2 815.5p 0.0000Log-likelihood −14546.0N 384,865

Note: *p < 0.05; **p < 0.01; ***p < 0.001. Status Quo is the reference category. Peace years cubic splinevariables not shown. Standard errors are robust standard errors adjusted for clustering within dyads.



The other key variables continue to be positive and significant acrossall three equations. Therefore, perfect deterrence theory’s predictions of StatusQuo, Defender Concedes, Challenger Defeated, and Conflict are all stronglysupported by the empirical record, and these predictions are robust againstalternative explanations.

The results for the control variables are mostly in line with previouslyestablished expectations. The balance of forces has a positive coefficientthroughout, although it is not significant for the Challenger Defeated equa-tion. Distance, democracy, and peace years all reduce the probability ofeach non-status quo outcome, although democracy is surprisingly not sig-nificant for the Challenger Defeated equation. The S score only has a signif-icant impact on Challenger Defeated, which is in the expected negativedirection.

These results for the prediction of game outcomes are more easilyunderstood through examination of predicted probabilities. The value forthe predicted outcome is set to 1, the values for the other outcome predic-tions is set to 0, and the control variables are set to their means.

TABLE 3 Multinomial Logit Results with Control Variables

Outcome

VariableDefender Concedes

Challenger Defeated Conflict

Predicted Status Quo b −0.1890 −0.0977 −0.1294Seb 0.1288 0.2009 0.1492

Predicted Defender Concedes 0.4295*** 0.4415* 0.21900.1140 0.1632 0.1203

Predicted Challenger Defeated 1.3692*** 1.3851*** 1.4294***0.2344 0.2798 0.1949

Predicted Conflict 0.8118*** 1.0545*** 1.0342***0.1173 0.1978 0.1783

Balance of Forces 0.5442*** 0.0294 0.2714*0.1057 0.1967 0.1368

S Score −0.3201 −0.9355** 0.37060.2430 0.3493 0.3805

ln(Distance) −0.2670*** −0.2478*** −0.3968***0.0135 0.0199 0.0190

Minimum Democracy −0.0248*** −0.0137 −0.0224*0.0059 0.0102 0.0108

Peace Years −0.2146*** −0.1312*** −0.2959***0.0203 0.0305 0.0246

Constant −3.2696*** −4.0878*** −3.2657***0.2463 0.4480 0.3546

c2 2315.6p 0.0000Log-likelihood −13145.0N 380,292

Note: *p < 0.05; **p < 0.01; ***p < 0.001. Status Quo is the reference category. Peace years cubic splinevariables not shown. Standard errors are robust standard errors adjusted for clustering within dyads.



Table 4 shows the impact of outcome predictions on the predictedprobabilities of outcomes. To ease interpretation, the Status Quo column ofTable 4 shows the predicted probability of each outcome given a predictionof Status Quo. The other columns show the change in the predicted proba-bility of a given outcome when a non-status quo outcome is predicted. Forexample, predicting Defender Concedes decreases the probability of StatusQuo by 0.19%, increases the probability of Defender Concedes by 85.71%,and increases the probability of Challenger Defeated and Conflict by50.00% each.

Prediction of any non-status quo outcome reduces the probability ofthe Status Quo, although not by the largest of margins. The prediction of aconcession by Defender greatly increases the probability of a Defender Con-cedes outcome (an increase of over 85%), the prediction of a defeat forChallenger greatly increases the probability of Challenger Defeated (anincrease of 300%), and the prediction of Conflict has a large impact on theprobability of Conflict (an increase of 250%). Each of these results is in linewith expectations.

Astute readers will note that although predictions of Defender Concedesand Conflict have their largest impact on the appropriate outcome, they alsogreatly increase the probability of other non-status quo outcomes. Thisshould actually be expected, since each of the equations is a comparisonbetween a non-status quo outcome and the status quo. When a non-statusquo outcome is predicted, it should make the status quo less likely to occur.If the status quo is less likely, then all non-status quo outcomes (even thosenot specifically predicted) are more likely.17

17Thus, the key results are the direction and significance of the outcome predictions on those outcomes(e.g., of predicted Defender Concedes in the Defender Concedes equation). Note that each of these coef-ficients is positive and highly significant.

TABLE 4 Impact of Outcome Predictions on the Predicted Probabilities of Outcomes

Predicted outcome

OutcomeStatus Quo

Defender Concedes

Challenger Defeated Conflict

Status Quo 0.9978 −0.19% −0.80% −0.41%Defender Concedes 0.0014 85.71% 364.29% 164.29%Challenger Defeated 0.0004 50.00% 300.00% 175.00%Conflict 0.0004 50.00% 425.00% 250.00%

Note: These predicted probabilities were calculated using the results of the full model (Table 3). Thevalue for each predicted outcome was set to 1, the values for the other outcome predictions set to 0,and the control variables were set to their means.



Nonetheless, prediction of Challenger Defeated has a larger impact onthe Defender Concedes and Conflict outcomes than on the ChallengerDefeated outcome. This indicates that the model has some difficulty in dif-ferentiating between concessions by Challenger and Defender. However,Wald tests for combining outcomes confirm that the model is able to distin-guish between each of the outcomes, again significant at the <0.0001 level.

A further test of the model’s empirical fit is provided by block tests ofstatistical significance, as shown in Table 5. These tests clearly demonstratethat the full model provides a better fit than the null model. Furthermore,removing any single equilibrium prediction produces a significantly worsefit to the data than the full model, as does removing the set of all four equilib-rium predictions. Thus, we can have confidence that each outcome predictionof perfect deterrence theory provides an important contribution to explain-ing the dynamics of deterrence.

One unusual feature of this test of perfect deterrence theory is that thetheory does not provide unique outcome predictions in most cases; rather,because of multiple equilibria, two or three different outcomes are possiblein many observations. Table 6 helps to clarify the empirical implications of

TABLE 5 Block Tests of Statistical Significance

Variable removed df Log-likelihood Probability

(Null Model, constant only) – −15397.22 –(Full Model) 36 −13608.77 <0.0001 (vs. null model)All 4 equilibrium variables 12 −13938.39 <0.0001 (vs. full model)Predicted Status Quo 3 −13613.57 0.022Predicted Defender Concedes 3 −13639.44 <0.0001Predicted Challenger Defeated 3 −13747.94 <0.0001Predicted Conflict 3 −13699.36 <0.0001

TABLE 6 Comparison of Predicted and Observed Outcomes

Observed outcome Percent correct

Predicted outcome(s) SQ DC CD DD Total Total Non-SQ

SQ 282,875 633 158 466 284,132 99.56 –SQ, DC 21,391 110 21 41 21,563 99.71 63.95SQ, DC, CD 3,435 51 10 51 3,547 98.56 54.46SQ, DC, DD 5,750 30 12 25 5,817 99.48 82.09SQ, CD 6,698 59 14 28 6,799 98.72 13.86SQ, DD 11,503 53 15 31 11,602 99.82 31.31DC 36,377 148 31 78 36,634 0.40 57.14DD 14,683 54 17 17 14,771 0.12 19.32Total 382,712 1,138 278 737 384,965 86.26 48.66

Note: Outcomes are abbreviated as follows: SQ: Status Quo; DC: Defender Concedes; CD: ChallengerDefeated; DD: Conflict.



these nonexclusive equilibrium predictions. Each row shows the number ofobservations that correspond to each group of predictions from Table 1,separated by the outcome actually observed. Thus, for example, there are21,563 observations where the predicted outcome is either Status Quo orDefender Concedes; of these, 21,391 actually result in the status quo, and afurther 110 result in a concession by Defender, for a total accuracy rate of99.71%. One can see that each of the predictions is about 99% accurate,except for the unique predictions of Defender Concedes and Conflict, whichare less than 1% accurate.

Clearly, the accuracy of these latter predictions is problematic. AsTable 1 makes clear, these unique predictions of Defender Concedes orConflict occur when Challenger prefers Conflict to Status Quo. In thatcase, Challenger’s only rational course of action is to challenge the statusquo, leading to one of those outcomes. This is the prediction of perfectdeterrence theory; however, it must also be the prediction of any theory,since that is the only logical result of those preferences. This result isclearly a product of error in the measurement of utilities. For instance, despitethe maintenance of the status quo throughout, Conflict is the predictedoutcome for the United States→Canada dyad for the period 1920–1941,because throughout, the United States is measured to prefer Conflict tothe Status Quo. While the United States almost certainly did not truly havethat preference, it is the best estimate produced by the measurement ofutilities employed here, based on the method pioneered by Bueno deMesquita and Lalman (1992). Bueno de Mesquita and Lalman (1992:298)acknowledge that the procedures they developed “may introduce consid-erable measurement error,” concluding that this “suppresses . . . ourresults.” Hence, future research should seek to improve our measurementof utilities; once that is done, one would expect support for perfect deter-rence theory to be even stronger.

Since non-status quo outcomes are rare events, one could achieve 99%accuracy by simply predicting the Status Quo for every observation. However,in so doing, one would achieve 0% accuracy of non-status quo predictions.As one can see from Table 6, the non-status quo predictions here are about49 percent accurate (with the accuracy of individual predictions between 14and 82 percent accurate). Thus, perfect deterrence theory provides a pro-portional reduction in the error of non-status quo predictions of 20 percent.Although improvement is always possible, these results nonetheless supportperfect deterrence theory.

These results for perfect deterrence theory can be put in perspectiveby comparing them with an alternative theory of international conflict.Bueno de Mesquita and Lalman (1992) constructed the International Inter-action Game to analyze relations between states. Although this is not theway they present it, theirs is essentially a theory of general deterrence.Furthermore, it has been extensively tested by Bennett and Stam (2000b) in



a multinomial logit analysis quite similar to that conducted here. Therefore,it is useful to compare the results found here to the results obtained byBennett and Stam.

Only five outcomes emerge as equilibrium predictions of the Interna-tional Interaction Game: status quo, acquiescence by A, acquiescence by B,negotiation, and war. However, six different outcomes of the IIG—statusquo, acquiescence by B, negotiation, capitulation by A, capitulation by B,and war—are realized. Thus, one equilibrium prediction (acquiescence by A)never occurs in reality, and two other outcomes that do occur (capitulationby A and capitulation by B) are never predicted in equilibrium. In the Uni-lateral Deterrence Game, however, all four possible outcomes occur in bothpredictions and the historical record.

In addition, the multinomial logit results obtained here provide muchstronger support for perfect deterrence theory than the support Bennett andStam (2000b) found for the International Interaction Game. As Bennett andStam (2000b:473) note, only two of the equilibrium predictions “are helpingto differentiate non-status quo outcomes from the status quo.” Compare thisto the Unilateral Deterrence Game, where each outcome prediction helps todifferentiate between the status quo and non-status quo outcomes. If perfectdeterrence theory is more consistent with the empirical record than “one ofthe most important theories of international conflict” (Bennett and Stam2000b:451), then one must take note.

CONCLUSIONS

A divide exists in the literature between formal theories and quantitativeanalyses of deterrence, largely because formal theories of general deter-rence have never been subjected to direct empirical testing. This paper hassought to bridge this divide in two ways.

First was to develop the conceptualization and procedures to makesuch direct empirical testing possible. Key conceptualizations include caseselection for direct general deterrence—I argue that identifying opportunityfor conflict is the key. In addition, procedures to measure the actors’ utilitiesfor the different outcomes were developed. Also, since incomplete informa-tion equilibria depend on each state’s estimate of the opponent’s credibility,a nonlinear transformation technique was developed to estimate the credi-bility parameters.

Using these procedures, I have endeavored to fill a large void in the lit-erature by testing perfect deterrence theory, focused on the theory’sUnilateral Deterrence Game with incomplete information. I used multino-mial logit methods to examine the prediction of particular game outcomes.The results indicate that the theory is well supported by the historicalrecord.



The results of this research have important policy implications as well.The policy recommendations of perfect deterrence theory and classicaldeterrence theory are diametrically opposed on many issues (Zagare 2004).For example, classical deterrence theory argues that national missile defenseundermines the stability of deterrence (for example, Powell 2003), whereasan application of perfect deterrence theory demonstrates that national missiledefense enhances deterrence stability (Quackenbush 2006b). However, policydiscussions in academia and government are generally based on classicaldeterrence theory. Given its strong empirical support, coupled with logicaland empirical limitations of classical deterrence theory (Zagare 1996),perfect deterrence theory would provide a much better basis for analyzingvarious aspects of national security policy. This could be done by applyingperfect deterrence theory to case studies of particular events (for example,the analysis of the war in Kosovo by Quackenbush and Zagare 2006) or tothe analysis of particular policy issues (for example, the analysis of nationalmissile defense by Quackenbush 2006b).

In addition, perfect deterrence theory provides a natural basis for furtherempirical research on the dynamics of deterrence. First, future researchfocused on improving measurement of utilities would be particularlypertinent. Also, direct tests of further formal theories—not only theories ofdeterrence—are of vital importance for improving our understanding ofinternational interactions. In addition, this analysis was focused on only oneof the theory’s three core models, applied across all observations. Thus, thisanalysis may have underestimated the theory’s explanatory power. Oneavenue for future research is therefore to conduct a more nuanced test incor-porating models of mutual and extended deterrence. And finally, further the-oretical expansions of perfect deterrence theory—such as an incorporationof more nuanced bargaining elements like endogenous stakes—wouldgreatly improve our understanding of the dynamics of deterrence.

REFERENCES

Beck, Nathaniel, Jonathan N. Katz, and Richard Tucker. (1998) Beyond OrdinaryLogit. American Journal of Political Science 42(4):1260–1288.

Bennett, D. Scott, and Allan C. Stam. (2000a) EUGene: A Conceptual Manual. Inter-national Interactions 26(2):179–204.

Bennett, D. Scott, and Allan C. Stam. (2000b) A Universal Test of an Expected UtilityTheory of War. International Studies Quarterly 44(3):451–480.

Bennett, D. Scott, and Allan C. Stam. (2000c) Research Design and EstimatorChoices in the Analysis of Interstate Dyads: When Decisions Matter. Journal ofConflict Resolution 44(5):653–685.

Bennett, D. Scott, and Allan C. Stam. (2005) EUGene Documentation, v. 3.1. Avail-able at http://eugenesoftware.org



Bremer, Stuart A. (1992) Dangerous Dyads. Journal of Conflict Resolution 36(2):309–341.

Bueno de Mesquita, Bruce. (1975) Measuring Systemic Polarity. Journal of ConflictResolution 19(2):187–215.

Bueno de Mesquita, Bruce. (1985) The War Trap Revisited. American Political ScienceReview 79(1):156–177.

Bueno de Mesquita, Bruce, and David Lalman. (1992) War and Reason: Domesticand International Imperatives. New Haven: Yale University Press.

Danilovic, Vesna. (2001) Conceptual and Selection Bias Issues in Deterrence. Journal ofConflict Resolution 45(1):97–125.

Danilovic, Vesna. (2002) When the Stakes are High. Ann Arbor: University of MichiganPress.

Diehl, Paul F., and Gary Goertz. (2000) War and Peace in International Rivalry.Ann Arbor: University of Michigan Press.

Fearon, James D. (1995) Rationalist Explanations for War. International Organization49(3):379–414.

Fearon, James D. (2002) Selection Effects and Deterrence. International Interactions28(1):5–30.

Ghosn, Faten, Glenn Palmer, and Stuart A. Bremer. (2004) The MID3 Data Set,1993–2001. Conflict Management and Peace Science 21(2):133–154.

Green, Donald P., and Ian Shapiro. (1994) Pathologies of Rational Choice Theory: ACritique of Applications in Political Science. New Haven: Yale University Press.

Huth, Paul K. (1988) Extended Deterrence and the Prevention of War. New Haven:Yale University Press.

Huth, Paul K. (1999) Deterrence and International Conflict: Empirical Findings andTheoretical Debates. Annual Review of Political Science 2:61–84.

Huth, Paul K., and Bruce Russett. (1984) What Makes Deterrence Work? Cases from1900 to 1980. World Politics 36(4):496–526.

Huth, Paul K., and Bruce Russett. (1988) Deterrence Failure and Crisis Escalation.International Studies Quarterly 32(1):29–46.

Huth, Paul K., and Bruce Russett. (1990) Testing Deterrence Theory: Rigor Makes aDifference. World Politics 42(4):466–501.

Huth, Paul K., and Bruce Russett. (1993) General Deterrence between EnduringRivals: Testing Three Competing Models. American Political Science Review87(1):61–73.

Jones, Daniel M., Stuart A. Bremer, and J. David Singer. (1996) Militarized Inter-state Disputes, 1816–1992. Conflict Management and Peace Science15(2):163–213.

Marshall, Monty G., and Keith Jaggers. (2002) Polity IV Project: Political RegimeCharacteristics and Transitions, 1800–2002. http://www.cidcm.umd.edu/inscr/polity

Morgan, Patrick M. (1983) Deterrence: A Conceptual Analysis. 2nd edition. BeverlyHills: Sage.

Powell, Robert. (1990) Nuclear Deterrence Theory: The Search for Credibility.Cambridge: Cambridge University Press.

Powell, Robert. (2003) Nuclear Deterrence Theory, Nuclear Proliferation, andNational Missle Defense. International Security 27(4):86–118.



Quackenbush, Stephen L. (2006a) Identifying Opportunity for Conflict: PoliticallyActive Dyads. Conflict Management and Peace Science 23(1):37–51.

Quackenbush, Stephen L. (2006b) National Missile Defense and Deterrence. PoliticalResearch Quarterly 59(4):533–541.

Quackenbush, Stephen L., and Frank C. Zagare. (2006) Game Theory: ModelingInterstate Conflict.” In Making Sense of IR Theory, edited by Jennifer Sterling-Folker. Boulder, CO: Lynne Rienner.

Russett, Bruce M., and John R. Oneal. (2001) Triangulating Peace. New York: Norton.Schelling, Thomas C. (1960) The Strategy of Conflict. Cambridge: Harvard University

Press.Schelling, Thomas C. (1966) Arms and Influence. New Haven: Yale University Press.Schultz, Kenneth A. (2001) Democracy and Coercive Diplomacy. Cambridge:

Cambridge University Press.Senese, Paul D., and Stephen L. Quackenbush. (2003) Sowing the Seeds of Conflict:

The Effect of Dispute Settlements on Durations of Peace. Journal of Politics65(3):696–717.

Signorino, Curt S. (1999) Strategic Interaction and the Statistical Analysis of Interna-tional Conflict. American Political Science Review 93(2):279–297.

Signorino, Curt S. (2003) Structure and Uncertainty in Discrete Choice Models. PoliticalAnalysis 11(4):316–344.

Signorino, Curt S., and Jeffrey M. Ritter. (1999) Tau-b or Not Tau-b: Measuring the Sim-ilarity of Foreign Policy Positions. International Studies Quarterly 43(1): 115–144.

Signorino, Curt S., and Ahmer Tarar. (2006) A Unified Theory and Test of ExtendedImmediate Deterrence. American Journal of Political Science 50(3):586–605.

Singer, J. David, Stuart Bremer, and John Stuckey. (1972) Capability Distribution,Uncertainty, and Major Power War, 1820–1965. In Peace, War, and Numbers,edited by Bruce Russett. Beverly Hills: Sage.

Snyder, Glenn H. (1961) Deterrence and Defense: Toward a Theory of NationalSecurity. Princeton: Princeton University Press.

Sorokin, Gerald L. (1994) Alliance Formation and General Deterrence: A Game-Theoretic Model and the Case of Israel. Journal of Conflict Resolution38(2):298–325.

Weede, Erich. (1983) Extended Deterrence by Superpower Alliance. Journal ofConflict Resolution 27(2):231–254.

Zagare, Frank C. (1990) Rationality and Deterrence. World Politics 42(2):238–260.Zagare, Frank C. (1996) Classical Deterrence Theory: A Critical Assessment. Inter-

national Interactions 21(4):365–387.Zagare, Frank C. (2004) Reconciling Rationality with Deterrence: A Re-examination

of the Logical Foundations of Deterrence Theory. Journal of Theoretical Politics16(2):107–141.

Zagare, Frank C., and D. Marc Kilgour. (2000) Perfect Deterrence. Cambridge:Cambridge University Press.



APPENDIX

I briefly detail the equilibria and measurement details here; complete dis-cussions are provided in an online appendix at http://web.missouri.edu/∼quackenbushs/

Unilateral Deterrence Game Equilibria

Zagare and Kilgour (2000) model incomplete information by allowing eachplayer to be uncertain of the other player’s type. Challenger estimates theprobability that Defender is Hard, pDef, and Defender estimates the proba-bility that Challenger is Hard, pCh (where 0 < p < 1 in each case). They findfour major types of perfect Bayesian equilibria. Each equilibrium specifiesvalues for four important parameters: xH (xS) = probability that a Hard (Soft)Challenger defects at node 1, and yH (yS) = probability that a Hard (Soft)Defender defies at node 2. Certain Deterrence equilibria exist where [xH, xS;yH, yS] = [0, 0; 1, *] when pDef ≥ ct; Steadfast Deterrence equilibria exist where[xH, xS; yH, yS] = [0, 0; 1, u] when pDef < ct; Separating equilibria exist where [xH,xS; yH, yS] = [1, 0; 1, 0] when cs ≤ pDef ≤ ct; Bluff equilibria exist where [xH,xS; yH, yS] = [1, v; 1, u] when pDef < cs and pCh < dn; Attack equilibria existwhere [xH, xS; yH, yS] = [1, 1; 1, 0] when pDef < cs and pCh ≥ dn. The region ofexistence for each equilibrium is defined by a combination of three criticalpoints. These critical points, defined below, are necessary to empiricallygenerate the equilibrium predictions tested here:

Measurement Details

Three important changes are made here to Bueno de Mesquita and Lalman’smeasurement procedures. First, I use Signorino and Ritter’s (1999) measure offoreign policy similarity, S, as the basic building block for these measurementsof utility. Secondly, I constrain the political cost term to be non-negative toprevent this “cost” term from providing an artificial boost to the utility forConflict. Therefore, I use the equation .

The third important change in Bueno de Mesquita and Lalman’s mea-surement techniques made here deals with the costs borne by a state in givingin (gx) compared to the costs borne by a state in conflict (wx). While Buenode Mesquita and Lalman simply assume that gx = wx = 1, this sets the cost ofbacking down equal to the cost of fighting. Unfortunately, this assumptionmakes Conflict preferred to concession in almost all circumstances. In other

cc c

c cc

c c

c cd

d d

d dtDC SQ

DC DDs

DC SQ

DC CDn

CD DC

CD DD

=−

−=

−−

=−

−+ −; ; .

fx xmax[u (SQ),0]=



words, if it is assumed that gx = wx, then almost all possible threats are cred-ible. Clearly this is a problem; states often prefer to back down rather thanfight, since the costs borne by a state in giving in are generally less than thecosts associated with conflict. Therefore, it is assumed here that gx = 0.25and wx = 1.

With these modifications to the procedures laid out by Bueno de Mesquitaand Lalman (1992), each state’s utilities for each outcome are measured. Theindividual components of these utilities are calculated using EUGene (Bennettand Stam 2000a). These raw utility values (which can range from −3 to 2) arenormalized to the interval from 0 to 1.

Since I am testing predictions based on incomplete information condi-tions where player types are not common knowledge, Challenger’s estimateof the probability that Defender is Hard (pDef) and Defender’s estimate ofChallenger’s type (pCh) are needed. I develop a nonlinear transformation ofthe difference between the utility for conflict and a concession, which I callΔU = U(conflict) – U(back down), to the interval between 0 and 1 whilealso accounting for the impact of risk propensity. These credibility estimatesfor each player are measured as

pe

ep

ec c

c c

R d dDef

Ch Def

DD CD

DD CD

DD DC

=+

⎡

⎣⎢

⎤

⎦⎥ =

−

−

+ −3

3

1 3

1

( )

( )

( ) ( )

11 3

1

+

⎡

⎣⎢

⎤

⎦⎥−

+

e d d

RCh

( )

( )

.DD DC


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