Few decisionmaking environments arefraught with greater risk than the anarchyof the international system. The fact thatbad foreign policy choices hold the poten-tial for disaster (e.g. war) is alone justifi-cation for the considerable time spent bystudents of international politics on thelogic of military deterrence. Most researchon deterrence assumes that states are
rational. Meanwhile, accumulating empiri-cal evidence from laboratory experimen-tation suggests that decisionmakerssystematically violate the strict behavioralexpectations of rationality. As anarchyplaces state survival at risk, these findingsfrom cognitive psychology similarlythreaten international relations theory andsupport the growing call for new models of
international politics grounded in the
capacities of actual decisionmakers.Initially developed by Daniel Kahnemanand Amos Tversky (1979), prospect theoryis an empirical model of decisionmakingthat stands as the ‘leading alternative toexpected utility as a theory of choice underconditions of risk’ (Levy, 1996: 179). It istherefore well suited to a re-examination of deterrence. In contrast to rational choice,prospect theory finds that decisionmakers
do not maximize in their choices, are apt tooverweight losses with respect to com-parable gains, and tend to be risk aversewhen confronted with choices betweengains while risk acceptant when confrontedwith losses. Considerable research onprospect theory outside political scienceexists, and scholars studying internationalpolitics have recently taken it up. Still, thegrowing recognition that actors choose asprospect theory suggests, and not as ourtheories of deterrence often assume, has not
Department of I nternati onal Affair s, Uni versi ty of Georgia
Prospect theory is an empirical model of choice that stands as the leading alternative to rationality forexplaining decisions under conditions of risk. While many still defend the assumption of rationality asan appropriate starting point for the construction of international relations theory – deterrence theory
especially – there is growing support for models of international politics grounded in the actual capac-ities of real-world decisionmakers. This article accepts that standard depictions of deterrence incentivescapture much of the essential character of deterrent relationships. However, it substitutes cognitiveassumptions in place of traditional rational choice. Using prospect theory, the article reconsiders threetypical deterrence games. The new model of military deterrence put forth unearths a set of conditionsthat are required for successful deterrence and uncovers a set of causes for deterrence failures that runcounter to conventional understanding.
* I am indebted to the comments of the anonymous review-
ers and to the generous help of Robert Grafstein. Pleasedirect correspondence via e-mail to [email protected]
yet forced a thorough review of deterrencetheory and practice.
This article presents a new theory of deter-rence that is grounded in the actual capacitiesof decisionmakers. It accepts the standard
depiction of deterrence incentives while sub-stituting a cognitive model of decisionmak-ing for rational choice. Using prospect theoryas a cornerstone, three types of deterrence arereconsidered: mutual deterrence, unilateraldeterrence, and extended deterrence.Prospect theory identifies a new set of con-ditions that are required for successful deter-rence, and uncovers a new set of reasons forthe failure of deterrence that run counter toconventional understanding.
The academic literature on deterrence islarge, but the number of core arguments issmall. This article addresses the core whilesetting aside the important body of work thatextends or modifies the basic set of premisesthat constitute deterrence theory.1 Thepurpose here is to return to the core andbegin rebuilding a foundation that incorpor-
ates an empirically supported model of human decisionmaking. Accordingly, theargument addresses (and adopts) some of thesimpler examples of game theory in the studyof deterrence. Working at this elemental levelis a necessary first step toward the full expres-sion of a formalized theory of cognitive deter-rence.
The argument below unfolds as follows.After a brief discussion of rationality and cog-
nition, I present a short summary of typicalconcerns about traditional deterrence theory.Prospect theory is then introduced as analternative foundation for understanding thedynamics of deterrence behavior. A generaldeterrence model is developed and then usedto re-examine three common deterrence
games. Finally, I highlight the unintendedconsequences of deterrence threats that arerevealed under prospect theory but hidden byrational choice.
Relative Strengths: RationalityVersus Cognition
While the behavioral expectations of prospect theory differ from rational choice,prospect theory retains a principal advantageof rational analysis. Actor decisions are stableand predictable. Earlier psychologicalapproaches to the study of internationalrelations depended heavily upon the personaltraits of individual decisionmakers, uponinformation flows unique to the decision set,or upon a unique group dynamic in thedecision setting.2 By contrast, prospecttheory permits the construction of hypoth-eses that cut across contexts; it thereby co-opts simplicity as the principal benefit of rational models. This is likely the reason forits growing recognition in political science.
Broadly, research on cognition and deci-sionmaking demonstrates that individualchoices are as much a function of consistentheuristics and biases as they are the result of calculated costs and benefits. Prospect theoryis part of this larger investigation into thestructure of human choice.3 It is the mostwell-traveled finding to emerge, and it hasbeen successful at penetrating other fields inwhich human decisionmaking is important
(e.g. political science and economics). Devia-tions from rationality are not treated as excep-tions; they are instead important phenomenafor which an explanation is possible. There isalready considerable empirical evidence that
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1 Such extensions are too numerous to mention, butinclude topics like the logic of first strike (Wagner, 1991);deterrence in the developing world (Kraig, 1999); the
potential value in promoting proliferation (Bueno deMesquita & Riker, 1982); critiques of US policy (Jervis,1984b).
2 For a discussion of psychology and foreign policydecisions, see Vertzberger (1990). For examples of psychol-ogy in the deterrence literature, see Lebow (1989) andJervis, Lebow & Stein (1985).3 For a summary of the major findings, see Kahneman &
Tversky (1982) and Bell , Raffa & Tversky (1988). For agood non-technical summary of this literature, see Plous(1993).
prospect theory can capture importantaspects of state behavior (Levy, 1992;Farnham, 1994; Levy, 1996; Berejikian,1997; Farnham, 1997; McDermott, 1998),suggesting that it is a solid foundation from
which to build a theory of deterrence.Increasingly, the use of classic rationality as
a foundation for international relationstheory – or any political theory – is contested.Time constraints, huge amounts of infor-mation, and uncertainty, combined with cog-nitive limitations, make it difficult for foreignpolicy actors to evaluate all possible scenariosand make a universally rational choice. Oneresponse to this critique is that classic ration-ality can be replaced with ‘satisfying’ or a‘bounded’ conception of rationality. The ideahere is to utilize an assumption closer to theactual process of decisionmaking while retain-ing the benefits of rational choice models,namely their parsimony and predictivebreadth. However, scholars in the field of deterrence have largely adopted a secondposition. This view argues that all theories are
abstractions from a complex reality. What isimportant is not the truth of the assumptionsimbedded in the theory but the explanatorypower of the model.4
But the explanatory power of rationalchoice explanations is itself often questioned.For example, Simon (1983) first noted thatmuch of the explanatory work of rationalmodels comes not from the ‘Herculean’assumption that people strictly maximize,
but from a rich set of auxiliary claims aboutwhat people want and how they view theworld. Similar arguments are found in theinternational relations literature. The dangerof emphasizing rationality lies in ‘drawingattention away from the areas that containmuch of the explanatory “action” in whichwe are interested’ (Jervis, 1988: 325).5 Thisargument penetrated to the heart of political
science. It lies, for example, at the center of Elinor Ostrom’s Presidential Address to theAmerican Political Science Association,which challenged political science to developa behavioral theory of collective action.
According to Ostrom, theories of politicsshould be ‘based on models of the individualconsistent with empirical evidence abouthow individuals make decisions in social-dilemma situations’ (Ostrom, 1998: 1). Theapplication of findings from cognitive psy-chology to the study of deterrence is con-sistent with Ostrom’s call to the discipline.The most productive theories of politics willbe those built upon the actual characteristicsof individual choice.
Still, rational deterrence has establisheditself as a powerful anchor for both theoryand practice, producing a framework that has‘dominated postwar academic thinking onstrategic affairs’ and lies at the core of the‘intellectual framework of Western militarypolicy’ (Achen & Snidal, 1989: 143). Ulti-mately, some blend of rational and cognitive
models will provide scholars with a compre-hensive understanding of military deter-rence. Recent developments in formal theoryare suggestive.6 Rational and cognitive deter-rence can coexist as complementary pieces of a larger whole. For example, the model to beoffered below treats threat credibility asexogenous: it is assumed that deterrencethreats range from highly credible to largelyincredible. Using formal tools, Nalebuff
(1991) demonstrates that a central com-ponent of threat credibility lies in rival per-ceptions about the hidden costs of action.The lower the hidden costs, the greater theactual strength of a state and the greater itswillingness to implement threats. The key tomaintaining credibil ity is the proper manipu-lation of rival perceptions about hidden coststhrough the judicious use of threats andaggression. Too much or too little of either
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4 For a general defense of this position, see Waltz (1990).5 For a discussion of formal rational choice in securitystudies, also see Walt (1999).
6 The debate over the utility of formal models in securitystudies is ongoing (Brown et al., 2000).
can damage a state’s reputation and inviteaggression. This model of credibility for-mation and maintenance thus suppliesimportant pieces of the larger deterrencepuzzle not provided by cognitive deterrence.
Conversely, cognitive deterrence can fill gapsexisting in some formal models. Fearon’s(1994) interest-signaling model suggests asequence game wherein challengers selectthemselves into or out of deterrence crises.Interestingly, defenders with solid repu-tations will nonetheless often fail to deterhighly motivated challengers, a finding con-firmed by the analysis below. However, theorigins for motivation in the signaling modelare exogenous: states are assumed to possesshigh or low levels of motivation. Under theframework of cognitive deterrence offeredhere, a state’s motivation will be explained byits level of risk acceptance.
More immediately, the question posed bycognitive psychology to the study of inter-national politics is compelling. Rather thanasking if traditional rationalist assumptions
are useful for theory construction, we shouldask whether or not it still makes sense to con-tinue with a model of choice that we know tobe beyond the capacity of real-world actors.The question becomes more pressing giventhat we have at our disposal cognitive modelsthat are in fact accurate descriptions of theactual process of decisionmaking.
Problems with Deterrence TheoryThe logic of military deterrence is commonlydepicted as a game of chicken.7 Here eachstate has two choices. The first is to supportthe status quo through cooperation. Thesecond is to overrun the status quo throughmilitary action. The universe of possible
outcomes is given in Figure 1. If both co-operate, the status quo continues. If one statedefects, deterrence has failed. I f both defect,war is the result. The standard assumption isthat each side prefers an advantage over itsrival to the cooperative status quo, thougheach prefers the status quo to open conflict.Stripped to its core, successful deterrencerests in effectively communicating a willing-ness to impose heavy costs upon a rival if itpursues unacceptable policies.
The dilemma for states in such games isthat each has an initial incentive to move off the status quo. This undermines the credi-bility of deterrent threats because ‘having tocarry out this threat if deterrence fails hurts
the threatener, even though the threat itself iswhat is supposed to prevent deterrence fromfailing in the first place’ (Brams & Ki lgour,1988: 46). We should then observe animmediate race to defection by both statesbecause the first to defect gains a strategicadvantage. But deterrence often does work.In response, proponents of traditional deter-rence theory offer several explanations for thestability often observed in deterrence
relationships.One line of reasoning holds that states can
deliver credible commitment threats. Statesrationally commit to a deterrent strategy if inthe long run such a commitment brings ahigher expected payoff than no commitment.The assertion boils down to the following:
It is rational to execute the intention [toretaliate] if and only if it is utility maximizing
to form it. From this follows that since it maybe rational to form the intention to execute thethreat, it may also be rational to carry it out
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7 While this metaphor is commonly associated with deter-rence, other incentive structures may also capture thedynamics of deterrence games. For example, Zagare (1987)
suggests that deterrence games are best represented by theprisoner’s dilemma. For simplicity of presentation, thegame of chicken will be assumed throughout.
. . . . if the intention has been formed, anddeterrence fails, then a rational agent whointends to retaliate should do so because actingupon this intention is part of the behaviorrequired of an expected utility maximizer.(Zagare, 1990: 252)
The argument here is that deterrence suc-ceeds when both states are able to communi-cate the fact that each intends to undertakeaction that is irrational at the time it must betaken, but rational at the time the commit-ment is made.
Many find this an unsatisfying solutionthat clouds rather than clarifies the logic of deterrence. If deterrence should fail, ‘it isirrational to retaliate, even on a probabilisticbasis, because retaliation leads to a worseoutcome for the threatener, having to carryout his threat, as well as for the player whopreempted and thereby provoked retaliation’(Brams & Ki lgour, 1988: 46).8 Alternatively,states might deploy a tripwire as a signal of resolve in order to increase the credibility of deterrence threats. However, the compara-
tively small losses incurred by sacrificing thetripwire troops should not, under rationaldeterrence, lead to a decision to accept themuch larger costs of war.9 Others suggest thatstates can form preferences for irrationalactions – like responding to an attack – andthat once formed such preferences are usuallycarried out (Gauthier, 1984). Critics cor-rectly note that this opens a Pandora’s boxwherein states are free to create preferences
for all kinds of irrational goals. Once statesare permitted irrational goals, there are notheoretical restrictions on the sort of irrational behavior they can undertake. Thedeductive power of deterrence theory rests in
the assumption that states are rational;without that assumption, prediction is lost.
Similarly, empirical studies have producedwidely different results and little or no con-sensus on a set of variables that predict
successful deterrence (Jervis, 1989; Harvey,1995). Early findings demonstrated that therelative size of the threatening state is of littleimportance. Military inferiority is not asufficient deterrent (Zinnes, North & Koch,1961). Indeed, evidence suggests aggressorsoften understand that they are militarily infe-rior, that they would lose an all-out war, andthat aggression on their part significantlyincreases the probability of a war (Russett,1967). One possible explanation is thatdefender states will sometimes fight tomanipulate their reputation for toughness.However, there are theoretical reasons tobelieve that such attempts are likely to provecounterproductive (Jervis, 1984a), andempirical results confirm that states that havefought in the past are no better at deterringrivals then those states that have not (Huth &
Russett, 1984). Additionally, many factorsassociated with deterrent behavior are them-selves not often predicted by the theory. Forexample, the greater the level of target dis-satisfaction with the status quo, the less effec-tive deterrence threats are. One explanation isthat dissatisfaction offsets ‘perceptions of insufficient capability’, thus leading toaggression even in the case where smallerstates face more powerful rivals (Zinnes,
North & Koch, 1961: 470). But contem-porary deterrence theory would deny thisresult. A state dissatisfied with the status quoshould not, under rational deterrence, under-take a course of action that would causefurther deterioration or decline in position.
Most deterrence scholars argue that anempirical consensus will follow with furthertheoretical development (e.g. Achen &Snidal, 1989), and agreement over the oper-ationalization of key terms (e.g. Huth &Russett, 1990). Meanwhile, critics remain
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8 Nalebuff (1991) uses formal logic to demonstrate thatstates may find retaliation rational because it enhancesreputation. My analysis assumes that states are not playingreputation games.9 It is possible that tripwires are one way in which states
might create so-called ‘audience costs’ in the domesticpolity, creating an incentive to respond (Fearon, 1997). Butthis has not been empirically established.
convinced that deterrence theory must berecreated, rather than simply patched, if it isto provide important guidance to stateshoping to avoid conflict (George & Smoke,1989; Lebow, 1989). The growing call for
behavioral theories of politics firmlygrounded in the actual capacities of real-world decisionmaking, combined with thetheoretical and empirical difficulties found instandard deterrence theory, suggests the needfor a reworking of military deterrence theoryalong cognitive lines.
Prospect Theory
Critics of contemporary deterrence theoryalso argue that often states simply fail tomake rational choices. Empirical worksupports this claim (Jervis, Lebow & Stein,1985). For some, this suggests that the foun-dations for rational deterrence theory aresuspect, while others argue that any deduc-tive model of deterrence is inherently flawed(Steinbruner, 1983). However, that second
position is correct only if non-maximizingbehavior is random, so that deterrent threatselicit no predictable response from the targetand therefore that states have no way toestablish a good strategy. Indeed, both sup-porters and critics of deterrence theory tendto equate non-rational behavior with unpre-dictable choices. By contrast, prospect theorysuggests that non-rational choices are bothstable and predictable. This makes a deduc-
tive theory of deterrence possible.The cornerstone for prospect theory lies in
the observation that, subjectively, there is adiminishing return to continually increasinggains. For most people, an initial windfall of $1,000 is more highly valued than is the same$1,000 when added to an initial gain of $10,000. That is, the value function for indi-viduals with respect to gains is concave, rep-resenting a curvilinear relationship betweenincreasing gains and subjective value. Asimilar relationship exists for losses such that
the value function for losses is convex. Theprincipal distinction between prospecttheory and rational choice lies in this asym-metrical relationship between gains andlosses. Expected utility theory holds that
decisionmakers evaluate the desirability of outcomes against their net asset position, andhave a single function against which bothgains and losses are evaluated. By contrast,the core finding under prospect theory is thatdecisionmakers evaluate each choice anewand against a neutral reference point (Kahne-man & Tversky, 1979; Thaler, 1980). Ratherthan a single utility function against which alloutcomes are evaluated, decisionmakersinstead have two such functions, one forgains and one for losses.
This relationship is given in Figure 2. Thegraph’s origin represents the reference pointagainst which gains and losses are evaluated.The s-shaped form of the value function cap-tures the diminishing relationship betweenobjective gains and losses with subjectivevalue. Note also that the value function for
losses is steeper than for gains. Losses hurtmore than a gain feels good, or as Kahnemanand Tversky put it, this steeper losses curvereflects the ‘observation that a loss has agreater subjective effect than an equivalentgain’ (Kahneman & Tversky, 1982: 166).
There are two important implications of this model for the study of internationalpolitics. The first is the so-called framingeffect. The essentials of framing can be
described with an example lottery.
• Gains frame : Imagine a choice betweentwo options that imply personal gains.Option 1: a sure gain of $80. Option 2:a risky venture with an 85% chance of winning $100 and a 15% chance of winning nothing. When confrontedwith this choice, most prefer the suregain to the risky venture although theexpected monetary outcome is $5 less.
• Losses frame : Now imagine a second set
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of options that imply personal losses.Option 1: a sure loss of $80. Option 2:an 85% chance of losing $100 and a15% chance of losing nothing. Hereindividuals prefer the gamble to the surething although the expected monetaryloss is $5 greater.
This finding is quite robust. Studies deliber-
ately designed to refute it have reconfirmed thebasic result (Grether & Plott, 1979). Termedpreference reversal, this flip in preferences isnot predicted under rational choice because itviolates the principle of invariance. It shouldnot matter how prospects are framed; underrational choice, individuals ought to be con-sistent in their preferences no matter how theyare presented. Because expected utility theoryassumes that individuals evaluate gains andlosses against net asset positions and along asingle utility function, it predicts that
individuals might be either risk averse or riskacceptant across choices, but not both.
Preference reversal also breaks with therational model in that the decisional determi-nant is not the expected outcome, but how thechoice is perceived relative to the status quo.Individuals do not maximize even when theyhave perfect information. Indeed, in animportant sense, objective outcomes become
unimportant because ‘the same decision can beframed in several different ways and differentframes lead to different decisions’ (Kahneman& Tversky, 1982: 165). Figure 3 plots thes-shaped utility function over the set of gainsfor the hypothetical lottery given above. Noticethat in the gains quadrant, an individual wouldprefer a sure gain of $80 to an 85% chance towin $100.10 Prospect theory predicts, and
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Subjectivevalue (+)
Subjective
value (–)
Losses Gains
$500 gain
$500 loss
Figure 2. Subjective Utili ty Functions under Prospect Theory
10 In the losses quadrant, the same individual would preferthe gamble offering an 85% chance of losing $100 to acertain loss of $80.
empirical results confirm, that decisionmakersare risk averse when confronted with choicesover gains and risk acceptant when confrontedwith choices over losses.
The second implication of the s-shaped
value function is loss aversion. In Figure 2,the negative value of a $500 loss is subjec-tively greater than the positive value of anequivalent gain. Loss aversion implies thatdecisionmakers will act more aggressively toavoid a loss than to secure an equal gain, andwill pursue loss aversion beyond a rationalexpectation of benefits. The tendency here isto place a greater value on that already pos-sessed compared with equivalent goods notyet acquired. This finding is consistent withan observed endowment effect, which is alsosupported empirically. Here, individuals con-sistently overvalue that which they alreadypossess such that the endowment effect‘enhances not the desirability of what one
owns, but the pain of forsaking it’ (Nincic,1997: 99).
Prospect theory thus models the subjec-tivity of actual decisionmaking. An indi-vidual’s attitude toward risk is not simply a
function of expected outcomes. Rather, riskdisposition is influenced by ‘whether the out-comes are perceived as gains or losses’ relativeto a reference point (Quatrone & Tversky,1988). The important idea here is that ourtheories of deterrence lag behind our know-ledge of human decisionmaking. Risk accep-tant and non-maximizing behavior is notintegrated into models of deterrence, despitethe fact that this is sometimes how decision-makers act. For example, under prospecttheory, the deployment of deterrence threatscan have several unintended consequencesthat are not predicted by rational deterrence.Credible threats might generate a lossesframe for the target state and thereby push it
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into risky behavior. The target of a threatmight then risk breaking off negotiationswhen the threatening state was simplyattempting to secure a better deal. Or, threatsmay induce the target to attack even if there
is only a low probability of success. This isexactly the sort of behavior the initial threatwas intended to deter. All of this is exploredin detail below. The point here is that ourunderstanding of decisionmaking under riskis quite different with prospect theory as theassumed model of choice.
Deterrence and Decision Frames
The framing effect identified under prospecttheory suggests that state assessments aboutthe attractiveness of the status quo play acentral role in explaining deterrence behav-ior. If continued mutual deterrence is accept-able, then states confront a choice betweenselecting the known benefits of the status quoor pursuing a gamble intended to furtherimprove their position through defection.
When this gamble contains an expected valueof further gain but also some probability of loss (i.e. open conflict), the state would be ina gains frame. Prospect theory predicts thatthe state would forgo the opportunity toimprove its position and opt for the certaintyof the status quo. Conversely, a state operat-ing under an unacceptable status quo also hasan opportunity to improve its positionthrough defection. When this gamble con-
tains an expected value of further loss, butalso some probability of approaching anacceptable status quo, the state would be in alosses frame. Prospect theory predicts that thestate would accept the gamble.
This produces a general theorem for deter-rence: deterrence is more likely to be effective when both states are in a gains frame, and less likely to be effective when either or both are in
a losses frame . Under gains, a state will not risk
disturbing the status quo even if the expectedvalue of defection is greater than continued
cooperation, so long as there is also somesmaller probability of loss. This means thatunder a gains frame, even less than perfectlycredible deterrence threats will provide asufficient deterrent. By contrast, in a losses
frame, states will risk defection even if theexpected value of this strategy is less thancontinued cooperation, so long as there is achance that this course of action will returnthem to a condition of normalcy.
Prospect theory does not predict thecontent of the decisional frame, that is,whether a state views the status quo of deter-rence as acceptable or unacceptable. A state’sassessment of the status quo is an empiricalquestion. As a guide, one could look to recentchanges in a state’s strategic condition.Assuming a near-perfect correlation betweena state’s objective condition and its percep-tion of that condition, changes in the statusquo would then provide a guide to thecontent of the decisional frame.11 However,decisionmakers also possess unique world-views. Documenting the content of the
frame therefore requires evidence about thestate’s actual condition and a reconstructionof decisionmaker perceptions. Political sub- jectivity thus plays an important role in ananalysis using prospect theory. The possi-bility of a cognitive frame – that is, whereonly the perception of the state is operativeregardless of objective circumstances – is con-sistent with the observation that the referenceagainst which outcomes are evaluated is the
condition to which ‘one has become adapted’and that there are many cases in which it is
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11 Depending upon the nature of change, a gains or lossesframe will exist for some period after change has occurred.The speed with which updating takes place, that is, ‘howlong one retains an original point of reference’ in assessingthe value of recent change, is an important question forprospect theorists, but one that is little understood (Shafir,1992: 316). Jervis, for one, suggests that it takes longer toincorporate losses into the reference point than gains(Jervis, 1992: 200). This tendency is at best a guide to
empirical research, not an ironclad theory of updating.Ultimately, a state’s assessment of the status quo is anempirical question; it cannot be pre-specified theoretically.
‘determined by events that are only imagined’(Kahneman & Tversky, 1982: 171–172).Thus, states may have a view of their circum-stances that has few connections to reality.However, the existence of a purely subjectiveframe would require thorough documen-tation.
Prospect Theory and Deterrence
Mutual Deterrence
Traditionally, the incentives for a deterrencegame like that given in Figure 1 are rep-resented using ranked preferences. Unfortu-nately, ranking outcomes does not tell us if
either state is satisfied with the deterrentstatus quo as is required for an analysis usingprospect theory. The matrix tells us thatmutual cooperation is preferred relative tounilateral cooperation and mutual defection,but not whether it is a set of conditions withwhich the state is ultimately satisfied.
Instead of ranked preferences, intervalpayoffs allow the introduction of status quoassessments while retaining the incentive
structure given in Figure 1. This permits adirect comparison of traditional and cogni-tive deterrence. Consider Figure 4a. Cellpayoffs depict state assessment of the variousoutcomes in comparison with what each per-ceives to be an acceptable condition. Positivevalues represent increases in satisfaction overan acceptable status quo. Negative values
represent dissatisfaction with outcomes: thelarger the negative number, the further a stateis from an acceptable condition. We can nowrepresent the same set of relationships givenin Figure 1 and introduce the notion of areference point.12 In standard deterrencetheory, open conflict is the worst possibleoutcome, and the one both sides wish toavoid most. It is possible then that statesfinding themselves here would view theircondition as unacceptable. The value –1given to this cell is meant to represent that itis unattractive compared with the deterrentstatus quo. Of course, a larger negative valuewould be possible, say, if we were comparing
conventional deterrence to nuclear deter-rence.13 But this would not alter the under-lying dynamics of the game. Figure 4b alsorepresents the logic of mutual deterrence,only here the status quo of cooperation isunacceptable to both states. Consistent withthe standard game, open conflict is worsestill, while unilateral cooperation sitsbetween open conflict and mutual deter-rence. In this game, the only acceptable
outcome for each state is unilateral defection.
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12The transition to interval payoffs offered here retains the
preference order for chicken games as given in Figure 1.From this point forward, the analysis assumes intervalpayoffs for both cognitive and rational deterrence.
Figure 4a. Mutual Deterrence in a Gains Frame Figure 4b. Mutual Deterrence in a Losses Frame
13 It has been suggested that at the extremes of ‘very smallprobabilities or for catastrophic losses’ the framing effectmay break down because it is overwhelmed by the distri-bution of costs and benefits attendant to the choice set(Levy, 1995: 3). In nuclear deterrence, it may be that thepotential costs of aggression are so large that they do in factoverwhelm the framing effect. This raises an important dis-tinction between total versus limited nuclear war as deter-rents. The notion of a limited nuclear war suggests that thecosts of conflict are not beyond consideration. Therefore, itmay be that cognitive deterrence is appropriate for analyz-
ing limited war deterrents while rational choice is a betterguide to understanding total war threats. This issue clearlybegs further examination.
This use of interval payoffs to representdeterrent games does not alter the con-clusions reached by rational deterrencetheory discussed earlier. The preferenceorder in Figures 4a and 4b is identical, and
both reproduce the traditional deterrencerelationship given in Figure 1. Specifically,each state has an incentive to defect first andimpose a settlement upon its rival. Mutualcooperation is preferred to unilateralcooperation, and unilateral cooperation ispreferred to open conflict. Finally, as before,deterrent threats have to overcome the factthat once a rival defects the best strategy isto capitulate.
Under prospect theory, the two games arequite different. In Figure 4a, both states areconfronted with options implying gains andare therefore in a gains frame. Either may optfor the gains from the status quo, or gamblein an attempt to improve its position.14 Thecurrent benefits under the status quo areknown. Risk comes in attempting to improveone’s position at the expense of the other. I f
successful, this strategy produces furthergains. It also contains some chance of loss inthe form of open conflict. The choice set isanalogous to the example lottery given in theearlier discussion of prospect theory. Statesmay select a certain smaller gain or gamble inan attempt to improve their condition.
Prospect theory predicts that when twostates are in a gains frame (4a) they willhave a relatively easy time crafting a stable
deterrent relationship because the thresh-old for a successful deterrence threat is low.Under rational choice, if an aggressor cal-culates the expected benefits of defection tobe larger than cooperation, that state willattempt to overrun the status quo. Underprospect theory, even if the expectedbenefits of defection are greater thancooperation, states in a gains frame will
continue to cooperate so long as defectionalso risks losing the benefits enjoyed underthe status quo. This follows from theempirical findings under prospect theory.States in a gains frame are risk averse. That
is, they will accept certain smaller gains infavor of larger but less certain gains. Giventhe structure of deterrence games, no deter-rent threat is ever completely credible.However, under prospect theory, even i f weassume that each state views the deterrencethreats of the other to be less than fullycredible, so long as there is some (evensmall) chance that they will be executed,mutual deterrence will hold. As notedearlier, one of the dilemmas of deterrence isthat the underlying incentives place thecredibility of deterrence threats in doubt.Yet, deterrence often works. We begin hereto see why. For states under a gains frame,deterrence threats need not be ironclad toprove effective because states are cautiousand risk averse.
By contrast, in Figure 4b, neither state is
satisfied with the status quo. The optionsfacing these states are analogous to the hypo-thetical lottery discussed above for choicesinvolving loss. Each state may opt for thesmaller certain losses of the status quo, or itmay gamble and risk further loss in anattempt to return to a satisfactory condition.Unlike 4a, states in this game are risk accep-tant. They will defect even if the expectedbenefit from defection is less than the certain
value of cooperation, so long as defectionprovides some chance of approaching anacceptable status quo. Deterrence relation-ships under conditions of loss are quiteunstable. The risk acceptance that is gener-ated by loss suggests that even highly credibledeterrence threats are unlikely to be effectivedeterrents. This is in sharp contrast to statesin a gains frame, against which less credibledeterrents are sufficient.
Simply put, mutual deterrence is morelikely to work when both states are in a gains
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14 There is a third possibility here. Either state may beforced to consider responding to provocation from its rival.The dynamics of retaliation will be discussed below.
This fully resolves the dilemma identifiedearlier in traditional deterrence: there shouldbe a race to defection in deterrence games,but deterrence often works. Under prospect
theory, the important independent variablethat predicts the success or failure of deter-rence is each state’s level of satisfaction withthe status quo. States satisfied with the statusquo are not compelled to overrun it, as thetraditional interpretation of matrix payoffssuggested. Stated this way, the findings of prospect theory sound like common sense,and this should be considered a strength of the approach. Prospect theory does notrequire the kind of conceptual stretchingfound in traditional theory – for example, theargument that rational states bind themselvesto irrational deterrence commitments – inorder to explain state behavior.
Unilateral Deterrence
Unilateral deterrence exists where one state issatisfied with the status quo and another is
not (Zagare, 1987: ch. 3). Using the samecoding scheme as before, this relationship isdisplayed in Figure 5a. Here, X is the revi-sionist state while Y is the status quo power.The preference orders for each state followthe standard depiction of deterrence. Again,from the perspective of rational deterrence,
there are no important differences betweenthe dynamics of this game and thoseprevious. While the interval payouts are nolonger the same for each state, the order of preferences predicts that each has an incen-
tive to impose cooperation by defecting first.Under prospect theory, X and Y will each
react to this game differently. Specifically, Xwill be more successful in deterring Y than Ywill be in deterring X. Y is confronted withchoices implying gains. I t can either continueto enjoy the certain gains of the status quo orrisk open conflict by attempting to imposeunilateral cooperation. Because states in agains frame are risk averse, Y will forgo anopportunity to improve its position, even if this strategy is expected to produce furthergains, in favor of the certain smaller gains of the status quo. In short, Y’s risk aversion willlead it to support continued deterrence.
Meanwhile, X is in a losses frame and hastwo options. It can continue to cooperateunder an unacceptable status quo, or risk theeven greater losses of open conflict in an
attempt to impose unilateral cooperationupon Y. As X is in a losses frame and accord-ing to prospect theory risk acceptant, it ismuch more likely to attempt to override thestatus quo even if defection is expected toproduce still greater losses than continuedcooperation, so long as defection also con-tains the possibility of returning to an accept-able condition. Rational deterrence theoryhas demonstrated that the underlying struc-
ture of the game reduces the credibility of deterrence threats. Because deterrent threatsare always less than fully credible, there isalways some probability that Y will notretaliate. Stated differently, there is someprobability that defection by X will producean acceptable status quo. Confronted with achoice between certain smaller losses and agamble that produces less certain but largerlosses, and that also contains some smallchance of producing gains, X opts for thegamble, and for this reason that deterrence
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15 One version of rationalist analysis provides similar pre-dictions. The concept of mixed strategy equilibrium alsopredicts that deterrence is more likely to succeed in 4a thanin 4b. In 4a, the mixed equilibrium for mutual cooperationis .44 while in 4b it is .11. Further theoretical developmentis required, however, to establish mixed strategy analysis asa useful tool in understanding actual deterrence choices.Mixed strategies are derived by solving for the probabili tyof cooperative and non-cooperative plays that would makeone’s rival indifferent between offering cooperation anddefection (Morrow, 1994: 86). This seems to cut against thevery definition of real-world deterrence, where the idea isprecisely to convince the other side of the benefits of con-tinued cooperation. Additionally, it is difficult to imaginean actual decisionmaker randomizing cooperation anddefection choices along some probability distribution inorder to establish a long-run mixed strategy. For example,
this would mean that player X in Figure 4a would defect athird of the time regardless of the credibility of rival Y’sdeterrence threats.
fails. Under prospect theory, games of uni-lateral deterrence are like games of mutualdeterrence under a losses frame in that theyare unstable.
Now, if X defects, Y is faced with thechoice of capitulating or executing its deter-rent threat. Initially, conditions favor X.Because Y is risk averse, it is less likely to riskopen conflict in an attempt to return to amore favorable position. This line of reason-ing leads to the same conclusion reachedunder a traditional interpretation of thematrix. When faced with rival defection,states will capitulate. However, states oftenexecute their deterrence threats. An expla-
nation under prospect theory is possible.Defection by X will change Y’s assessment of the status quo. That is, the payouts in Figure5a demonstrate that an attack by X will pitchY into the upper right quadrant, and therebyinto a losses frame. The choices facing Y nowresemble the example lottery presentedearlier for choices involving loss. Y can acceptthe certain losses in the new status quo thatresulted from X’s provocation, or it can
retaliate. Retaliation involves a high proba-bility of even further losses (the bottom rightquadrant), but there is also the chance thatthe conflict might ultimately be resolved infavor of Y.
Defection in a unilateral deterrence gamecan therefore pitch the status quo state into alosses frame and induce risk-acceptantbehavior: in this context, that means execut-ing one’s deterrence threats. Prospect theorythus resolves a second deterrence paradox: Inthe face of aggression, why would any state
actually retaliate?Traditional theory suggeststhat states will act only if the expected valueof retaliation is greater than capitulation. So,for example, the notion that states retaliate inthe hope of a quick and favorable resolutionhas precedent in the development of rationaldeterrence theory (Zagare, 1987: chs 2, 3).Also, as noted above, states might retaliate toestablish reputations in future games.Prospect theory adds to this an understand-ing that retaliation is a risk-acceptant, non-maximizing choice motivated by a lossesframe.
While states do sometimes carry out theirdeterrence threats, they do not always do so.
Consider Figure 5b. Here, the object of dispute between states – say, a piece of terri-tory – has less strategic importance for Y thanfor X. Indeed, possession of the disputedterritory is a necessary condition of anacceptable status quo for X, but this is not sofor Y. Under these conditions, defection by Xwill not elicit retaliation from Y because itremains in a gains frame and is risk averse. Itshould be noted, however, that when targeted
with aggression states might revalue out-comes. For example, a strategically unimpor-tant concession may take on politicalimportance if the government fears inactionwill make the state look weak and unable tocarry through with its commitments, or if domestic political dynamics places pressureupon the government to act decisively. Anexample of the former might be the positionof NATO in the Kosovo crisis, and anexample of the latter might be the position of Great Britain in the Falklands war. A state’s
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reassessment of the status quo after loss maypitch it into a losses frame even though thestate previously attached little importance tothe issue.
In summary, unilateral deterrence
relationships are unstable. Revisionist statesfind the status quo unacceptable, and thisproduces risk-acceptant attempts to overridethe status quo through defection. Becausedeterrence threats are always less than fullycredible, there is always some chance thatdefection by revisionist states will produce anacceptable status quo. There seems little thata status quo power can do to improve theeffectiveness of deterrence threats leveledagainst risk-acceptant states. Incrementalincreases in credibility are likely to produceonly marginal results. Prospect theory alsoidentifies the conditions under which stateswill actually carry out their deterrence threatsand when they will not. The chance of retal-iation is greatly increased whenever aggres-sion pushes rivals into a losses frame.
Extended Deterrence Extended deterrence involves promising todefend an ally against aggression. The con-tinuing US commitments to Europe, SouthKorea and Taiwan are examples of extendeddeterrence. The analysis above suggests thatextended deterrence will be more effectivewhen the target of deterrence is in a gainsframe. Where the target views the status quoto be unacceptable and therefore becomes
risk acceptant, extended deterrent relation-ships will be quite unstable.
Extended deterrence games pose uniqueproblems and opportunities for patron states.Typically, patrons attempt to increase thecredibility of extended deterrence threats bypublic ironclad commitments to their ally.These usually come with a statement of thevital importance of the ally to the patron’snational security, and often include a signifi-cant commitment of military personnel onthe ground as an expression of seriousness.
While these actions are intended to increasethe credibility of an extended deterrent, theymay also solidify an existing losses frame inthe target. From the perspective of the target,patron support for rivals simply implies a
greater security threat. Indeed, this is thepoint of extended deterrence. However, asdemonstrated above, incremental increases incredibility and/or capacity are unlikely toprove compelling to states in losses frames solong as defection contains some chance of producing a satisfactory status quo. Thispossibility always exists in extended deter-rence games because it is harder to convincerivals that one will come to the aid of anotherthan it is to convince them that the state willdefend itself directly.
Nonetheless, introducing a third partyinto deterrence games opens the possibility of altering the target’s perception of the statusquo from losses to gains, thereby improvingthe prospects for successful deterrence. Thisis especially the case where a larger, morepowerful patron offers deterrence protection
to a smaller ally facing a similarly sized rival.Powerful patrons can dedicate some of theirconsiderable resources toward increasing thedesirability of the status quo. Economic aidor development assistance can be leveraged tonudge the target of extended deterrence intoa gains frame. An essential component of theCamp David peace accords was improvingthe desirability of the status quo to Egyptthrough economic assistance from America.
Of course, the level of commitment requiredby the patron may prove prohibitive. TheUSA, for example, seems unwilling to enterinto a series of Camp David agreementswhere it accepts a significant long-term econ-omic commitment to states engaged in con-flicts flung across the globe. Still, in theaftermath of the Cold War, the UnitedNations has become increasingly involved inpeacekeeping. Presumably, the burden of incentives could be shared. Moreover,while modern crises have required extending
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multilateral deterrence threats against poten-tial aggressors, recent experience in Bosnia,Kosovo and Iraq, to name but a few, suggeststhat the use of extended deterrence threats isalone insufficient to prevent conflict. The
analysis offered by prospect theory suggeststhat, in addition to these strategies, leadersshould also attempt to alter the target’s assess-ment of the status quo with inducements,and that this might reduce the need for actualmilitary force.
The US defense commitment on theKorean peninsula may provide an example.Historically, US strategy involved ongoingpublic commitments to defend the Southagainst the North, and the placement of amilitary force on the ground. The USA hasalso imposed economic sanctions. All this isintended to create pressure for reconciliationwith the South. However, as recent economicconditions in the North worsened, fears of open confrontation increased. Underprospect theory, this should be expected. Theundeniable effect of sanctions is that they
help create a losses frame and thereby risk-acceptant behavior. Recently, it appears thatUS policy has taken a new tack. A string of agreements between the North and the USA– for example, to upgrade North Korea’s civi l-ian nuclear power facilities and to loosensomewhat the economic sanctions inexchange for commitments to halt thedevelopment of ballistic missile technology –if continued, hold potential to lead North
Korea toward a more favorable reassessmentof the status quo. If successful, North Koreawill increasingly adopt risk-averse strategiesin its dealings with the South, reducing thepotential for conflict.
Deterrence Threats and LossesFrames
In addition to the deliberate manipulation of decisional frames, as discussed above, it is alsoconceivable that states inadvertently alter
rival frames. Most importantly, cognitivedeterrence opens us to the possibility thatthreats alone can produce a losses frame forthe target state, pushing rivals into risk-acceptant attempts to overturn the status quo.
It is canonical in the study of internationalpolitics that the natural result of one state’sattempt to make itself more secure is thecreation of a ‘security dilemma’ for rivals,making them less secure. Even seeminglydefensive preparations, under the self-helplogic of anarchic systems, create insecurity. Infact, the purpose of a potent deterrent threatunder the traditional view is precisely toproduce rival insecurity sufficiently com-pelling to deter unwanted action: to drain astate’s confidence about its capacity to suc-cessfully undertake aggressive actions. Thus,rival insecurity should lead to conservativepolicy choices. Bold, risky attempts to revisethe status quo bring forth the deterrent andresult in a loss for the state attempting to gainan advantage. One popular argument in thetraditional deterrence literature – a view
often echoed in the public policy discourseon deterrence – is that more deterrent isbetter. A deterrent capacity so large that it‘swamps all misperceptions arising, forexample, from cultural differences, indi-vidual idiosyncrasies, and the complexities of international politics’ is best (Steinbruner,1976: 227). Under prospect theory, this doc-trine of conservative planning, if it producesa losses frame where one did not previously
exist, may well be the road to disaster. Con-sider again two states operating under theincentives described in Figure 4a. Here, bothstates find the status quo acceptable. If Yattempts to significantly improve its deter-rence capacity, the security dilemma suggeststhat this act makes X feel less secure, leadingto a reassessment of the status quo. Onepossible outcome is a shift to Figure 5a whereX now views the status quo as unacceptable,is in a losses frame and risk acceptant, andtherefore more difficult to deter.
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Prospect theory thus forces a distinctionbetween credible threats and effectivemilitary deterrence. The two may not alwaysbe the same. Traditional deterrence theoryhas identified many factors that affect credi-
bil ity. They include the nature of political tiesbetween rivals and/or allies, the level of econ-omic interdependence between states, andpast actions in similar circumstances. Theutility of prospect theory is greatest in identi-fying the larger context within which credibledeterrents are likely to work best. In thislight, cognitive and rational theories supportone another. Under both, credible threats areimportant. However, cognitive deterrencesuggests that threats will be more effective,whatever their credibility, when the target of deterrence is not in a losses frame. The goal isto create credible threats but to avoid pro-ducing risk-acceptant behavior. Rather thanever more potent deterrents, an intermediatelevel of forces is best, sufficient to imposepenalties on a rival while not increasing itstolerance for risk.
Perhaps the central empirical implicationof cognitive deterrence is that a state’s assess-ment of the status quo, its decisional frame,should be given greater attention. Typically,the credibility of threats is viewed to be thekey independent variable explaining thesuccess or failure of deterrence. Under cogni-tive deterrence, perceptions about the costsand benefits inherent in the status quo are atleast as important a variable as threat credi-
bility. The possibility that deterrence threatscontribute to losses frames, and therebyproduce the very behavior that they areintended to deter, is a matter that clearly callsfor empirical investigation.
Conclusions
The strength of rational choice as an anchorfor international analysis lies in the construc-tion of an elaborate and sophisticated set of interrelated theoretical propositions about
the dynamics of international relations thatenjoy considerable empirical support. Bycontrast, prospect theory has not yet gener-ated an integrated set of theorems aboutinternational politics that might rival rational
choice. The purpose here is to construct anew set of propositions organized aroundprospect theory that apply to deterrence sothat a systematic empirical comparison of thetwo perspectives is possible. It would bewrong to suggest that this or any single articlereplaces the impressive set of propositionsalready constructed under rational choice.Instead, the purpose here is to demonstratethat it is possible to construct a logic of deter-rence with an empirically established modelof decisionmaking in a way similar to thatnow standing as the significant achievementof rational analysis in the study of deterrence.The next step is an orderly empirical investi-gation of the propositions offered above.
Several empirical strategies are possible.The simplest is to examine prominentinstances of deterrence failure to determine
if the aggressor was in a gains frame or lossesframe at the time deterrence collapsed. Theproblem with this approach is that it isvulnerable to spurious correlation. Forexample, we might observe aggression by astate that suffers under a losses frame, but if this behavior overlaps in time with a dimin-ished rival deterrent, then it is impossible todetermine which explanation – traditionalor cognitive – is best. Figure 6 summarizes
the predictions of cognitive and traditionaldeterrence by their key independent vari-able. Traditional deterrence theory arguesthat successful deterrence will continue solong as the capacity and credibility of eachstate’s deterrence threat remains unchanged,and that deterrence is most likely to failwhen the credibility of either state’s deter-rence threat diminishes. Prospect theory pre-dicts that deterrence will continue so long asneither state slips into a losses frame. Thisproduces four possible conditions for
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predict the same behavior in the upper leftand lower right cells, so an analysis of deter-rent behavior under these conditions revealslittle. A proper test would focus upon thatcombination of conditions under which thetwo theories differ in their predictions.
A still more compelling empirical strategyis offered in Figure 7, which produces con-ditions under which the two theories provideexclusive predictions. Under a losses frame
and an unchanged deterrent threat, prospecttheory predicts conflict while traditionaltheory predicts continued cooperation.Under a gains frame and diminished credi-bility, traditional theory predicts conflictwhile prospect theory predicts continuedcooperation. This case-selection strategyapproaches the ideal of a critical test becauseit permits us to control for the influence of each independent variable. If we find thatonly one theory is predictive in each of thesetwo conditions, then we can categorically
rule out the other theory as a possible expla-nation.
There is some evidence that such aninvestigation would prove fruitful. The pre-dictions from cognitive deterrence map onto
some of the earlier-noted empirical findings inthe deterrence literature. For example, the factthat powerful states often fail to deter weakerstates does not threaten cognitive deterrencetheory. When weaker states are in a lossesframe, they will be risk acceptant and moreprone to aggression. In addition, the findingthat excessive bullying diminishes deterrenceis also consistent with prospect theory. Con-ventional deterrence logic suggests that ahardline stance might be attractive to a stateattempting to establish credibility, and there-fore that such a strategy could be successful inimposing cooperation upon a rival. However,empirical results suggest that a ‘firm-but-fair’stance is more effective (Levy, 1989: 111). Thefact that firm-but-fair works does not by itself condemn traditional deterrence. The pointhere is that prospect theory has an explanation
for both the failure of bullying and the successof firm-but-fair. Between the two, bullying ismore likely to contribute to a losses frame forthe target and is therefore counterproductive.Bellicose diplomacy may increase the credi-bility of deterrence threats, but it may alsolead the target to the conclusion that someform of hostile rival action is forthcomingregardless of concessions. The status quo –updated for highly probable rival hostility – is
thus placed in a losses frame producing risk-acceptant behavior. Firm but fair deterrentthreats are less likely to generate this result,and thus are found empirically to be moreeffective.
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JEFFREY D. BEREJIKIAN, b. 1965, PhDPolitical Science (University of Oregon,1995): Assistant Professor, University of Georgia (1999- ); current research interestsinclude constructing a cognitive theory of
international politics.
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