FORCE AND RESTRAINT IN STRATEGIC DETERRENCE A GAME-THEORIST’S PERSPECTIVE pub823

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FORCE AND RESTRAINT IN STRATEGICDETERRENCE:

A GAME-THEORISTS PERSPECTIVE

Roger B. Myerson

November 2007

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This paper is based on a talk presented at the ChicagoHumanities Festival on Peace and War, November 11, 2006.

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ISBN 1-58487-325-6


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FOREWORD

This monograph is a short nontechnical introductionto the use of game theory in the study of internationalrelations. The focus is on the problem of deterrenceagainst potential adversaries and aggressors. Theauthor, Professor Roger Myerson, uses game models toprovide a simple context where we can see more clearlythe essential logic of strategic deterrence. We shouldlook to such theoretical analysis for basic insights thatmay have practical importance in policymaking.

The main conclusion is that a great powers useof its military forces may be rendered ineffectiveor even counterproductive when there are no clearinternationally recognizable limits on this use of force.Professor Myerson derives this conclusion from thebasic observation that our ability to inuence potential

rivals depends on a balanced mix of threats andpromises. Potential adversaries should believe thataggression will be punished, but such threats will beuseless unless they also believe our promises that goodbehavior will be better rewarded. A reputation forresolve makes threats credible, but a great power alsoneeds a reputation for restraint, to make the promisescredible as well. Thus, international restraints on anations use of military force may actually increasethe effective inuence of its military strength. Sothis monograph may be read as a contribution toour understanding of the vital relationship betweendiplomacy and military preparedness in defense ofnational security.

DOUGLAS C. LOVELACE, JR.DirectorStrategic Studies Institute


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BIOGRAPHICAL SKETCH OF THE AUTHOR

ROGER B. MYERSON, winner of the 2007 Nobel Prizein Economics, is the Glen A. Lloyd DistinguishedService Professor of Economics at the Universityof Chicago. He taught for 25 years in the KelloggSchool of Management at Northwestern Universitybefore going to the University of Chicago in 2001.Dr. Myerson is the author of two books and manyprofessional articles on game theory, informationeconomics, and economic analysis of politicalinstitutions. He is a Fellow of the American Academyof Arts and Sciences and has served as its Midwest VicePresident. Dr. Myerson was elected Vice President ofthe Econometric Society in 2006. He won a GuggenheimFellowship in 1983 and received an honorary doctorate

from the University of Basel in 2002. Dr. Myerson holdsa Ph.D. from Harvard University.


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SUMMARY

In a dangerous world, we need to think verycarefully about how military force is used. Gametheory can serve us in such analyses by providing aframework for probing the inextricable connectionsbetween our adversaries decision problems andour own. To illustrate the power of game theory,the author focuses on a vital question that confrontsAmerican policymakers today: What determines whyan application of military force, which was intendedto deter potential adversaries, sometimes insteadstimulates them to more militant reactions against us?When we feel that force is necessary, what can we doto minimize the risk of such adverse reactions?

A successful deterrent strategy is key and requires a

balance between resolve and restraint, and this balancemust be recognized and understood by our adversaries.So for our forceful actions to have their intendeddeterrent effect, they should be framed by a processof communication with our potential adversaries thatestablishes mutually recognized limits and rules aboutwhat we will and will not do.

From early roots in the work of John von Neumannand John Nash, game theory developed as a generalframework for analyzing systems of incentives thatinvolve two or more rational actors. Applications ofgame theory have extended beyond the traditionalscope of economics to include the design of auctions,incentives in organizations, analysis of politicalinstitutions, and problems of international relations. In

game-theoretic analysis of international relations, thegreat seminal classic is Thomas Schellings Strategy ofConict (Harvard University Press, 1960). In particular,


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the vital importance of our strategic coordinationwith our adversaries, as well as with our friends,

was shown by Schelling and is a fundamental pointof this paper. Indeed, all arguments herein may beviewed as straightforward applications or extensionsof Schellings ideas.


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FORCE AND RESTRAINT IN STRATEGICDETERRENCE:

A GAME-THEORISTS PERSPECTIVE

In a dangerous world, we need to think verycarefully about how military force is used. Game theorycan serve us in such analyses by providing a frameworkfor probing the inextricable connections betweenour adversaries decision problems and our own. Toillustrate the power of game theory, I focus here on avital question that confronts American policymakerstoday: What determines why an application ofmilitary force, which was intended to deter potentialadversaries, sometimes instead stimulates them tomore militant reactions against us? When we feel thatforce is necessary, what can we do to minimize the riskof such adverse reactions?

A successful deterrent strategy requires a balancebetween resolve and restraint, and this balance mustbe recognized and understood by our adversaries.So for our forceful actions to have their intendeddeterrent effect, they should be framed by a processof communication with our potential adversaries thatestablishes mutually recognized limits and rules aboutwhat we will and will not do.

From early roots in the work of John von Neumann(1928)1 and John Nash (1950)2, game theory developedas a general framework for analyzing systems ofincentives that involve two or more rational actors.Applications of game theory have extended beyondthe traditional scope of economics to include the designof auctions, incentives in organizations, analysis of

political institutions, and problems of internationalrelations. In game-theoretic analysis of internationalrelations, the great seminal classic is Thomas Schellings


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Strategy of Conict (Harvard University Press, 1960).In particular, the vital importance of our strategic

coordination with our adversaries, as well as with ourfriends, was shown by Schelling and is a fundamentalpoint of this paper. Indeed, all arguments herein may beviewed as straightforward applications or extensionsof Schellings ideas.

Intuitive Arguments Against MultilateralConstraints on American Actions.

Before making the case for strategic restraint, letme begin by citing some important expressions of acontrary view, against the acceptance of multilateralconstraints on Americas use of force. For example,consider the comments of President George W. Bushin September 2002, when a reporter asked his opinion

about Democratic senators who did not want toconsider the option of invading Iraq without a priordecision by the United Nations (UN). The Presidentresponded:

Democrats waiting for the U.N. to act? I cant imagine anelected member of the United States Senate or House ofRepresentatives saying, I think Im going to wait for the

United Nations to make a decision. It seems like to methat if youre representing the United States, you oughtto be making a decision on whats best for the UnitedStates. If I were running for ofce, Im not sure how Idexplain to the American people: Say, vote for me, and,oh, by the way, on a matter of national security, I thinkIm going to wait for somebody else to act.3

The logic of the Presidents view seems clear.

To defend ourselves against foreign threats, wemay sometimes need to use military force againstour adversaries, and any external constraint mightprevent us from using such force when we feel it is


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necessary. To protect American national security,American leaders have a responsibility to make these

vital decisions about American military actions, and itwould seem best for them to choose from the broadestpossible range of military options according to theirown best judgment. Accepting multilateral constraintsthat reduce the scope of American military optionswould seem counterproductive, like destroying partof our own military hardware, which was acquired atgreat expense to expand the capabilities of our forces.

In the Presidents view, this argument againstaccepting foreign constraints on American militaryactions seems so clear and so universal that thequestion of accepting UN restraint is not even worthdiscussing in an electoral campaign. He feels sure thatany attempt to defend a policy of accepting multilateralconstraints on American military actions would be a

losing political strategy.The President here was speaking off the cuff. It

might be worthwhile to consider also a careful articulateexpression of the argument against multilateralism byJonah Goldberg in 2006:

If it was right to topple Saddam Hussein, it was righteven if no one else agreed. If it was wrong, then it was

wrong even if the world was on our side. Lynch mobsarent right because they have numbers on their side,and men who stand up to them arent wrong becausethey stand alone. Multilateralism is good only to theextent that it allows us to achieve good things.4

The image of the lone defender of justice is a good one(although we might be a bit disturbed if our local police

chief actually applied this argument to rely on his ownbest judgment in arresting people, regardless of whatany judge or jury would say). Goldberg acknowledges


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that we might want UN approval if we needed theirhelp to conquer Iraq in the rst place. But if we can

beat Saddam Hussein on our own, he argues, then weshould ask no other question than whether it would begood or bad for us to do so.

This argument implicitly assumes that an invasionis intrinsically right or wrong, regardless of whatothers think. But a fundamental goal of our militarystrategy is to deter others from aggression against ourcountry. So the long-run success of a deterrent strategyfor protecting America depends on how foreignersthroughout the world will respond to our actions. Thus,if we care how others will react in the future, then wemay indeed want our decisions to take account of their judgments. This is the basic insight that I will try todevelop in this paper, using game theory.

In such questions of deterrence, where the best

strategy for us depends on how others will react to it,our strategic plan should be based on careful analysisof the actions that our potential adversaries will choose.But when we seriously endeavor to understand thechoices of our adversaries, we may realize that theirbest plan of action must be based on their analysisof how we are likely to react to them. So we cannotunderstand our decision problem or our adversariesunless we analyze our decisions and theirs together aspart of an inextricably connected whole. Game theoryhas been developed as a framework for analyzing suchinterconnected decision problems.

Game Theory as a Form of Analytical Narrative.

Game theorists study mathematical models ofsocial interactions. To be useful, a game model shouldbe simple enough to understand but should sharesome important similarities with the more complex


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situations of conict and cooperation that we facein real life. Game theorists use models as simplied

versions of life that are meant to clarify some of thelogic of lifes dilemmas, just as people everywhereuse stories to develop new perspectives on importantsocial problems.

People regularly tell stories to help themselves tounderstand society and its problems. To understandan international crisis, we might seek useful analogiesby retelling, for example, the story of the 1938 Munichappeasement (to justify resolve) or the 1962 Cubanmissile crisis (to justify restraint). In every culture,people have accumulated a wide repertoire of storiesthat are regularly retold as analogies that guidepeoples thinking about social problems. Of course,no story that we can tell will t any real situationperfectly. To overcome the limitations of one story, we

need to consider many stories, and the insights that weget from different stories must be compared. Models ingame theory are just stories of another kind.

As any literary form, game theory has stylisticconstraints which dene both the power and thelimitations of game theory. The people in the game arethe players, and each player in the game has to choosean action from a given set of alternatives. In the game,players have goals which are described numericallyby payoffs that depend on everybodys actions. It isassumed that each player wants to maximize his ownexpected payoff. Players may learn some informationin the game, and we can describe this possibleinformation in a game model by listing the set ofpossible observations with numerical probabilities for

each.So game theory requires a mathematically precise

description of what each person can do in the game and


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the preferences are that guide each persons choice ofaction. Such precision has the advantage that it makes

game situations very clear, but it requires us to eschewthe subtle vocabulary and imagery that enriches otherforms of story-telling.

In the analysis of such game models, game theoristsalways try to respect the players. In particular, weassume that the players are intelligent, in the sense thatthey understand everything that we game-theoristsunderstand about their game; and we assume that eachplayer is rational, in the sense that he will always choosehis own action to maximize his own expected payoff. Ingame-theoretic analysis, an equilibrium (as dened byJohn Nash) is a prediction of all players actions suchthat each players action is best for himself, given whatthe other players are predicted to do. Nash equilibriumis our basic solution concept for understanding what

people can rationally do in a game.

A Simple Model of the Strategic DeterrenceProblem.

To describe a dangerous world where incentives foraggression are pervasive, let us consider a version ofthe well-known Prisoners Dilemma game, shown inTable 1 below. This game involves two players, whomwe name simply A and B. For interpretation, letus say that player A represents America, and playerB represents some other smaller country in the world.In this basic game, each player must simultaneouslychoose one of two possible actions: cooperation oraggression. The payoff for each player depends on both

of their actions, as shown in the table. For each pair ofactions, Table 1 lists two numbers, the rst being Aspayoff and the second being Bs payoff.


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B cooperative B aggressive

A cooperative 0, 0 8, 1*

A aggressive *1, 8 * 3, 3*

As payoff, Bs payoff

Table 1.A Game with Pervasive Incentives forAggression (The Prisoners Dilemma).

The asterisks indicate the best payoff that each player

could get in response to each possible action of theother player. If B were expected to be cooperative, thenplayer A could get the payoffs 0 or 1 by cooperation oraggression, and so the best response for A is indicatedby the asterisk before As payoff 1 in the bottom-leftcell. On the other hand, if B were aggressive, thenplayer A could get the payoffs 8 or 3, and the best

response for A in this case is indicated by the asteriskbefore As payoff 3 in the bottom-right cell. The bestresponses for B to each of As possible actions aresimilarly indicated by asterisks after Bs payoffs, inthe top-right and bottom-right cells here. The cell thathas two asterisks is a Nash equilibrium of the game,because here each player is choosing his best response.In Table 1 we see that the unique equilibrium of this

game is in the bottom right, where both players areaggressive.

In the simple structure of this Prisoners Dilemmagame, each player nds his aggressive action to be hisbest response to each of the other players possibleactions, but each players choice of aggression ratherthan cooperation is very harmful to the other player.

So both players get payoff 3 in the unique equilibriumof the game. Of course, they would both be better offwith payoff 0 if both would cooperate, but mutualcooperation is not an equilibrium, as each player


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will always be tempted to aggression. The root of thedilemma here is that each player always gets at least a

small gain by switching from cooperation to aggressionhimself, but the result of such aggression will be a largeloss for the other player. So when the players have noopportunity to respond to each others actions in thisgame, each player wishes that the other player wouldact cooperatively but knows that he has no incentive todo so.

The analysis would change, however, if one ofthe players could observe the others action rst andrespond to it. If As decision to act cooperatively oraggressively could depend on what B chooses to do,then As reaction could give B some positive incentiveto cooperate. In this context, we can talk meaningfullyabout deterrent strategies.

A strategy for a player in a game is a complete plan

that species an action for the player in every possiblesituation that the player could encounter in the game.Modifying the game of Table 1, let us now suppose thatplayer A can observe whether B chooses cooperationor aggression before A makes his own choice betweencooperation and aggression. When player A getsto move second after observing what B does, playerA has four possible strategies which are listed inTable 2.

As strategy: Bs action: B cooperative B aggressive

A is cooperative always A cooperative A cooperative

A does the same as B A cooperative A aggressive

A does opposite of B A aggressive A cooperative

A is aggressive always A aggressive A aggressive

Table 2.The Four Strategies for Determining AsAction when A Can Observe Bs Prior Action.


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Now the outcome of the game will depend on Bschoice and As strategy as shown in Table 3 below. In

each cell, the payoffs are those from Table 1 when playerA chooses the action that is specied by his strategyagainst the given action of B. For example, when Asstrategy is do the same as B, if B is cooperativethen A is cooperative and the resulting payoffs (fromTable 1) are 0 for each; but if B is aggressive, then A isaggressive, and the resulting payoffs (again from Table1) are 3 for each.


A is cooperative always 0,0 8, 1*

A does the same as B 0,0* * 3, 3

A does the opposite of B *1, 8 8, 1*

A is aggressive always *1, 8 * 3, 3*As payoff, Bs payoff

Table 3.A Game Where Player A Moves afterObserving Bs Action.

In each row of Table 3, an asterisk after the secondnumber in a cell indicates that it is the best payoff thatB can get in response to the strategy of player A in this

row. Notice that a best-response asterisk appears afterBs payoff in the left B-cooperative column only for onestrategy, the strategy where A does the same as B. Soplayer A here has one deterrent strategy that motivatesB to act cooperatively, and that is the strategy where Adoes the same as B.

But is this deterrent strategy credible? When B is

cooperative, player A would get payoff 0 by doing thesame as B, but player A could get the higher payoff1 by using a strategy that is aggressive in this case.So A does not want to actually follow his deterrent


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strategy when B cooperates, so B should not believethat A would use this deterrent strategy, unless A can

somehow constrain himself to follow this strategy.Without such restraint, this game still has only oneequilibrium, where both players are aggressive andboth get 3.

So to induce B to cooperate, player A wants tomake a credible commitment to follow the deterrent(do same as B) strategy, but this commitmentrequires some outside force to restrain player A fromacting aggressively when B has cooperated. Thus,player A would prefer to enlarge this game by addingsome other players who could punish A for actingaggressively when B has cooperated. Such punishmentcan actually be achieved if A is expected to play similargames in the future, if the behavior of future opponentsin subsequent games can depend on how A behaves in

this game now.To be specic, let us suppose that player A will

play a game like the one in Table 3 every year but witha different player B each time. Suppose that player Ahas a reputation for using the do same as B strategyin these games, against which the B players should actcooperatively so that As payoff should be 0 in everygame. But if player A ever lost that reputation by actingaggressively against a cooperative B-player, then wemay suppose that the mutual-aggression equilibriumwould be played in all future games, yielding thepayoff 3 in all future games. At a 5 percent annualinterest rate, a income stream that pays $3 every yearwould be worth $60 in present discounted value(because depositing $60 in a bank account that pays

5 percent annual interest would allow you to take $3income every year forever). So As reputation in thisrepeated game should have a present value R that is


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approximately R=60. Subtracting this lost reputationalvalue from As payoff in the cases where A has acted

aggressively against a cooperative opponent, thecurrent game against the current player B looks likeTable 4. As long as the reputational value R is greaterthan 1, there is a good equilibrium in which B iscooperative and A does the same as B.


A is cooperative always *0,0 8, 1*A does the same as B *0,0* * 3, 3

A does the opposite of B 1R, 8 8, 1*

A is aggressive always 1R, 8 * 3, 3*


Table 4.As Reputation for Restraint Worth R>1 CanMake Deterrence Credible.

The game in Table 4 also has a bad equilibriumwhere everybody is always aggressive, and bothplayers get the bad payoff 3. Indeed, the threat ofswitching to such a bad equilibrium in the futureis what sustains the good equilibrium in Table 4. Sowith multiple equilibria, communication between

the players may help to get everyone focused on thebetter equilibrium, according to Schellings focal-pointeffect. That is, to coordinate everyones expectationson the good reputational equilibrium, player A mightannounce to the world:

We promise to be aggressive only when we have priorproof of our opponents aggression. If we ever deviate

from this promise, then you may expect us instead tobe aggressive always, so that all our opponents shouldbe aggressive against us if we break this promise evenonce. But as long as we maintain our reputation, our


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opponents should expect to gain by cooperating. So youshould be condent that we will rationally maintain ourreputation for restraint, because getting $0 always isbetter for us than getting $1 once and then $3 alwaysafterwards.

Thus A can benet from cultivating a reputation forrestraint in eyes of the world.

For this negotiation speech to be persuasive,however, everyone must anticipate that they would

not be persuaded by it again after A was seen deviatingfrom the terms of the promised strategy. If A could takeaggressive prots (1) against one cooperative B-playerand then persuade the next B player that they shouldresume the good reputational equilibrium where theBs all cooperate with A, then A would want to beaggressive every time. So the other future B players inthis repeated game all need to understand the promised

terms of As deterrent strategy, and they need toactively monitor As behavior and judge whether Ahas acted correctly according to this strategy.

Judging Reputations.

We have been assuming that when a player is

aggressive, the whole world will see that playersaggression. Let us consider what happens when thisassumption is dropped in the game in Table 4, whereplayer A has a reputation for restraint that has a largelong-run value R to player A. Suppose now that, if Bis aggressive, the whole world will probably see it,but there is some small positive probability that onlyplayer A will see Bs aggression and everyone else will

think that B has been cooperative. What should A doin a game where such a disagreement about B occurs?When the world thinks that B has been cooperative,


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it is better for A to be cooperative now and preservethe reputation than to be aggressive now and lose the

reputation (8 > 3 B R). As long as the probabilityof Bs aggression escaping general detection is not toolarge ( < 3/4 so that 1 + (1)3 < 0), the threat ofAs aggressive response when the world communityrecognizes Bs aggression should be sufcient to detersuch aggression.

On the other hand, the credibility of the deterrentstrategy could not be sustained if A were to actaggressively on private evidence that nobody elsecan observe. If A would not lose any reputation bybeing aggressive when the world sees no evidence ofBs aggression, then A would prefer to be aggressivealways, claiming always to be justied by privateevidence of Bs prior aggression; and so the deterrentstrategy would not be credible, as in Table 3. Thus, As

reputation must be judged by others.This important point deserves some emphasis.

We have argued that a nations military actions mustbe judged as part of a deterrent strategy, and this judgment cannot be made by the nation itself whenit has any ability to benet from such actions. In suchsituations, the jury that passes judgment on a nationsmilitary actions must be outside the nation itself.

Reputations for Restraint and Resolve.

The example in Table 4 is intended as a simplemodel of American foreign policy, with player Arepresenting America. In this model, we have adeterrent strategy that involves both a promise that

we will cooperate if our current rival cooperates, anda threat that we will be aggressive if our current rivalis aggressive. For our deterrent strategy to be effective,


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our rivals must believe our promise of cooperation. Butin the repeated Prisoners Dilemma game, we could

always get a short-run benet from acting aggressivelyinstead of cooperating. So to make our promises ofcooperation credible, we need some reputationalcommitment to act cooperatively when our deterrentstrategy promises it, and such a commitment is whatwe mean by restraint. So this model illustrates how thecredibility and effectiveness of Americas deterrentstrategy may require us to maintain a reputation foraccepting restraint from others in the UN.

Of course, an effective deterrent strategy alsorequires that our rivals must believe our threats ofpunishment as well as our promises of cooperation. Inother situations where ghting is costly and aggressionis unprotable, we might also need some reputationalcommitment to act aggressively when our deterrent

strategy threatens it, and such a commitment to actaggressively in such situations is what we mean byresolve. So a reputation for resolve may also be neededto make credible the threats that an effective deterrentstrategy also requires. Such a reputation for resolvewould be lost if we were ever seen to cooperate witha rival who had acted aggressively against us. Thenthe fear of losing such a reputation could give us anincentive to respond aggressively when we wouldotherwise nd it unprotable.

Which is more important: resolve or restraint? Inthe repeated Prisoners Dilemma game analyzed here,credible deterrence only required a reputation forrestraint. A reputation for resolve was unnecessary inthat game, because short-run incentives could always

motivate aggressive action. Of course, the PrisonersDilemma is just one simple model. More complicatedmodels can be formulated in which effective deterrence


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requires a reputation for resolve as well as a reputationfor restraint. But remember why the Prisoners Dilemma

interested us in the rst place: because the problem ofdeterring aggression becomes acute only to the extentthat individuals gain short-run prots from aggressiveactions that hurt others. If nobody ever had a problemof credible restraint from aggressive behavior, then wewould not have to worry about deterring aggressionin the rst place. So there is good reason to believethat restraint should be a signicant part of most realdeterrence problems.

One could argue, however, that resolve mightbe more important than restraint for small weaknations, because their weakness makes conict moredangerous for them. But stronger nations can nd moreopportunities for protable aggression, and so theymay have less need for resolve and correspondingly

more need for restraint. By this argument, we shouldexpect restraint to be most important for America,when America is the worlds most powerful nation.

For a simple example where resolve may be moreimportant, consider the game in Table 5 (which differsfrom Table 1 in that the 3 and 8 payoffs have beenswitched). Now each players best response is to beaggressive if the other player is cooperative (as 1>0),but to be cooperative if the other player is aggressive(as 3>8). So the paired asterisks in the bottom-left cell indicate an equilibrium where player A isaggressive and player B is cooperative, which is thebest possible outcome for A but is bad for B. But thereis also another equilibrium in the top-right cell whereplayer A is cooperative and player B is aggressive,

which is the best possible outcome for B but is badfor A.


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A cooperative 0,0 *3, 1*

A aggressive * 1, 3* 8, 8


Table 5.Game with Multiple Equilibria Where aReputation for Resolve Could Be Valuable.

For such games with multiple equilibria, Schelling

(1960) argued that anything in the players sharedculture or environment that focuses their attention onone equilibrium can lead them to act according to it,as a self-fullling prophecy. In particular, if player Ahas a reputation for being aggressive in such games,then B may naturally focus on the equilibrium thatplayer A prefers. Furthermore, if player A would

lose this valuable reputation by cooperating with anaggressive player B, then this reputation for resolvecould transform the game into one where the uniqueequilibrium is the outcome that player A most prefers,as shown in Table 6. But of course, if both playerstry to maintain a reputational commitment to actingaggressively in such games, then they would bothsuffer the worst payoff 8.


A cooperative 0,0 3 R, 1*

A aggressive * 1, 3* * 8, 8


Table 6.As reputation for resolve worth R>5 makes

B cooperative in equilibrium.


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On the other hand, Table 7 shows another variationon Table 5 in which player A is stronger than B, but

As strength is counterproductive because it effectivelystimulates Bs resolve. In this game, the strong playerA has an extra option to invade the other nation. If Ainvades when B is aggressive, then the outcome is thesame as if A were merely aggressive; but if A invadeswhen B is cooperative, then A enjoys a higher payoff of2 while B suffers a lower payoff of 9. Player B wouldstill be willing to cooperate if player A were simplyaggressive, but As temptation to turn aggression intoinvasion here eliminates any equilibrium where Bis cooperative. So player As extra option in Table 7makes this a game with a unique equilibrium, whichcoincides with the worst equilibrium for player A inTable 5. So the strong player A here is only harmed byhis ability to invade and could actually benet by an

external constraint that would eliminate this option forhim.


A cooperative 0, 0 *3, 1*

A aggressive 1, 3* 8, 8

A invades *2, 9 8, 8*


Table 7.The Perceived Danger of Being Invaded byA Makes B Aggressive in Equilibrium.

Failure of Deterrence: Stimulating Militarism byDenying Restraint.

More generally, we should ask, why might rationalcitizens prefer militant leaders who are committed tocostly military actions? People could have two natural


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motivations for such militarization: to protably attackothers, or to decrease their own chances of being

attacked. Most small countries in the world have fewopportunities for protable aggression, but a desirefor stronger defenses against possible attacks can bea motivation for people to seek militant leadershipin any country. Militant leaders can demonstrate theresolve that smaller countries especially need whenthey fear a possibility of invasion, as in Table 7. Soto decrease our neighbors incentives to militarizeagainst us, we want to reduce their fears of beingattacked. Our forceful acts without clear strategiclimits can counterproductively increase unconqueredadversaries militant commitment against us.

President Bush announced in September 2001 thatnations anywhere in the world that support terrorismwill be treated by the United States as hostile regimes.5

This proclamation may have sounded like a strongdeterrent strategy, but its effective implementationwould depend critically on who judges whether anation is or is not supporting terrorism. In the commentsquoted above, the President insisted that Americasleaders should make these judgments themselves,with no multilateral constraints. Thus, there should beserious questions about whether this broadly aggressivepolicy could fail as a deterrent strategy because of alack of clear restraint. Our demonstrated willingnessto preemptively invade a country on our own privateinterpretation of evidence, with no external constraintson our use of force, could be seen as a dangerousrepudiation of strategic restraint, which could inspirecounterforces against us (from guerrilla to nuclear,

depending on local capabilities).In particular, suppose that people in some nation

had some reason to think that America might want


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to attack them. Then they would naturally fear thatAmericas judgment about whether they support

terrorism could be swayed by American interestsagainst them, regardless of whether they have actuallysupported terrorism or not. Indeed, they might wellsee Americas 2003 invasion of Iraq as hard evidence ofthe possibility that they might also be so invaded. Butif they believe that such an American invasion is likely,no matter what they do, then they might rationallycalculate that their security could actually be enhancedby sponsoring global terrorism, to keep more Americanforces busy elsewhere in the world. They might alsoview their development of nuclear weapons as anotherway to improve their own security, by making thecontemplated invasion much riskier for America. Thus,Americas refusal to accept multilateral restraint couldactually exacerbate terrorist insurgencies and nuclear

weapons proliferation.So our theoretical models suggest that support

for global terrorism today might actually have beenless if the Bush administration had not conspicuouslyrejected UN restraint earlier in this decade. Of course,it is impossible to prove this hypothesis as we cannotrelive this decade with a different policy decision,nor can we compare this decade to an otherwiseidentical period when great-power leaders showedmore willingness to accept external restraint. So thesefundamental questions about the effectiveness of ourdeterrent strategies must be guided by logical analysis,and our conclusions may depend on the assumptionsthat we bring to our model. Other models with otherassumptions might lead to different conclusions. On

such important policy questions, we need a debate inwhich different models and views are compared.

But in September 2002, the Presidents expressedopinion was that accepting UN restraint on Americas


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military decisionmaking would be such a bad ideathat no responsible politician should even suggest

it, if he hopes to get reelected. As we have seen fromour models, however, there is good reason to thinkthat a reputation for accepting UN restraint may havebeen exactly what America needed to deter terroristaggression in this decade. The logic of our analysishere should be sufcient to make the case, at least, thatthe question of accepting UN restraint was worthyof serious political debate in America. It should nothave been mockingly dismissed by someone with aresponsibility to think about what is best for America.

For another recent example of a deterrent strategyexecuted without sufcient clarity of limits or restraint,we may consider the Israeli retaliation in Lebanonduring the summer 2006. Israeli bombing waswidespread and lacked any clearly articulated limits

or proportionality to the provocation. There was nodoubt that the kidnapping of soldiers was an aggressiveprovocation that required some strategic response; butthe heavy and unfocused nature of Israels responsecould raise questions about whether its intention wasto not merely deter specic acts of aggression butalso to change the nature of the regime in Lebanon toIsraels benet. Whatever the true intentions were, suchquestions could readily stimulate Lebanese fears of adeep invasion that would renew the violence of theircivil war. A natural response to such fears of invasionwould be to support militant parties who seem morecapable of ghting Israel. Thus, in the aftermath ofthe 2006 summer war, the leader of Hezbollah, HasanNasrullah, could preside over a huge rally in Beirut

where he posed as Lebanons strongest defender,calling 1200 Lebanese deaths in the recent war a smallprice to avoid Iraqs fate of 10,000 to 15,000 peoplekilled every month in a chaotic war incited by the


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Americans and the Mosad.6 Thus, ambiguity aboutthe limits of American and Israeli military actions may

have helped Hezbollah to sell itself as a strong defenderof Lebanons security.

Conversely, Arab calls for total elimination ofIsrael motivate Israelis to bear the high costs of theirmilitarization. People everywhere want securityagainst any perceived risk of a devastating invasion.Retaliatory actions and threats that lack clearly denedlimits can raise fears of deep invasions and thus canmotivate people on the other side to seek militantleadership that may be better able to defend them.Lack of clear restraint can stimulate others resolve.

Thus, if we want our application of military force todeter our potential adversaries, rather than stimulatethem to more militant reactions against us, then weshould make sure that the limits of our forceful actions

are clear to any potential adversaries. We need areputation for responding forcefully against aggression,but we also need a reputation for restraining ourresponses within clear limits that depend in a generallyrecognized way on the nature of the provocation. Theselimits must be clear to our potential adversaries, whomust be able to verify that we are adhering to the limitsof our deterrent strategy, because it is they whom weare trying to inuence and deter.

Reconsidering the Rationality Assumption.

Game-theoretic analysis is based on an assumptionthat people are rational. Of course nobody is perfectlyrational; we all make mistakes. But to get a sense of

what people are likely to do in any given situation,it is generally a good idea to think about what theirinterests are and to assume that they will act to pursue


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these interests. Our adversaries interests may bedifferent from our own, but we generally share at least

some common interests, such as avoiding the costs ofdestructive conict.

But it may be asked: What if our adversaries areirrational or congenital aggressors who cannot bedeterred? If so, what could we do but try to bindthem or destroy them? We should be very cautiousabout jumping to such conclusions. After all, if ouradversaries understood that we believed this aboutthem, so that our perceived self-interest would requiretheir destruction, then their struggle against us actuallycould become rational self-defense for them. Thuswe should not lightly contemplate such self-fulllingprophecies of congenital violence and mortal struggle.It is generally much safer to assume that our adversarieswill respond appropriately to a rm deterrent strategy

when our resolve and restraint are both made clear tothem.

Of course, there are people in the world who areirrationally or pathologically drawn to violence anddestruction. Our most dangerous adversaries are notlone madmen, however, but are leaders with politicalsupport from many people who have normal hopesand fears. Psychopathic militarists like Hitler becomea threat to our civilization only when ordinary rationalpeople become motivated to support them as leaders.

One might also question the game-theoreticassumption of selsh rationality when it is appliedto our own country. That is, we may ask: What if theassumption of selsh rationality does not apply to usbecause we can always be trusted to do what is right?

If so, then our intrinsic justice could be a sufcientdeterrent against aggression, and we would not need toworry about maintaining our reputation for appropriate


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restraint. But the effectiveness of our intrinsic justiceas an implicit source of restraint depends critically on

others believing in it. Our own belief in our own justiceis not enough.

Lessons for Patriots.

This paper has considered simple game-theoreticmodels to probe the basic logic of deterrence. Thelessons of this analysis may be briey summarized.

To inuence and deter potential rivals, we needa deterrent strategy in which threats of conict arebalanced by promises of cooperation when rivalsyield to our pressure. The threats and promises ofour deterrent strategy can be effective only if theyare understood and believed by our potential rivals.When Americans judge our leaders for effectiveness in

foreign policy, the central question should be how ourpolicy is perceived by the foreigners whom we wantto inuence and deter. Letting these foreigners judgeour reputation for adhering to our deterrent strategycan help us to guarantee its credibility. So a policy ofsubmitting American military actions to international judgment and restraint can actually make Americamore secure.

Any bomb by itself can only cause destruction.Our bombing can have a constructive purpose onlyas part of a strategy that denes when we bomb andwhen we do not bomb. But people have no incentive toyield if they think that their yielding would only invitefurther aggression and invasion. If our rivals do notunderstand the limits to our use of military force, then

our bombing can only spread destruction and resolveto resist us. So we want our adversaries to understandthe limits on our use of force, and we want them toverify that we are complying with these limits.


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Thus, we can benet from a reputation for acceptingstrategic limits on our use of force, using proportionate

retaliatory force only as necessary for deterring attackson us. But strategic communication is essential. Ourstrategic limits must be clearly communicated topotential adversaries, because our reputation for resolveand restraint is effective only to the extent that ouradversaries recognize it. For questions of whether ouruse of force has been appropriate under our deterrentstrategy, the ultimate judge and jury are the potentialrivals whom we want to deter and reassure. That is,on a question of whether a particular use of militaryforce was justied under our deterrent strategy, the judgment that counts is that of the foreigners whomwe want to deter. If our invasion has been justiedonly to American voters, then it has not been justiedat all.

It has sometimes been suggested that Americanswho doubt that everybody can always trust Americashould be denigrated as unpatriotic. Of course, patriotsshould have some basic faith in the good qualities ofour country, but that does not imply that patriots mustalways assume that everybody in the world will acceptour good faith without any proof or guarantee. As hasbeen argued above, ignoring foreign fears of our powerand denying any need for restraint can inadvertentlystimulate more militant reactions against us in theworld. So Americans who want to accept multilateralrestraints, to reassure foreigners about the limits of ourpower, may be true patriots who are asking the hardquestions that are essential to our national security.


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ENDNOTES

1. John von Neumann, Zur Theorie der Gessellshaftspiele(On the Theory of Parlor Games),Mathematische Annalen 1928.

2. John Forbes Nash, Jr., Equilibrium Points in N-PersonGames, Proceedings of the National Academy of Sciences, Vol. 36,1950, pp. 48-49.

3. President Bush discusses Iraq with reporters, September 13,2003, at www.whitehouse.gov/news/releases/2002/09/20020913.html .

4. Jonah Goldberg, When Multilateralism Falls Short,National Review, October 13, 2006.

5. In the Presidents address to Congress and the Americanpeople on September 20, 2001, at www.whitehouse.gov/news/releases/2001/09/200109208.html .

6. From Hasan Nasrullahs speech at a Hezbollah rally

in Beirut, September 22, 2006, at www.juancole.com/2006/09/nasrullahsspeechhereisbbcworld.html.

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