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3
Applications of Game Theory in Support of Intelligence Analysis

Bruce Bueno de Mesquita


Intelligence analysts are often asked to identify the likely—and unlikely—consequences of alternative courses of action for specific, real-time foreign policy problems. With limited time and potentially critical consequences, analysts must sort through the uncertainties surrounding the specific problem, providing a best estimate of what is likely to happen, estimating the probability of outcomes different from the best estimate, and assessing contingencies that might lead to alternative outcomes. In each instance, there is an interest to work through the logic of a situation to ascertain what might be done to alter or to facilitate particular outcomes. Keeping the intelligence assessment open to the prospects of a discontinuous change is especially important because the past is not a reliable predictor of the future (Feder, 2002; Fingar, this volume, Chapter 1).

The analyst’s task is daunting. Every case is fraught with unique features, the time for examining each case is limited, and the potential always exists for deleterious consequences if the analysis proves incorrect. Expert knowledge is the sensible starting place for understanding any specific case, but area or problem expertise should not be the only means of analyzing important, complex problems (Tetlock, 2005). Such expertise can be complemented by reliance on well-tested, rigorous methods of analysis. Such methods can provide an independent perspective that informs and stimulates debate.

I examine how game theory reasoning, combined with empirical, mostly quantitative, analysis, can help inform foreign policy analysis by (1) fostering reliable predictions about the likelihood of alternative outcomes and by assessing how alternative tactics and strategies might improve the expected



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3 Applications of Game Theory in Support of Intelligence Analysis Bruce Bueno de Mesquita Intelligence analysts are often asked to identify the likely—and unlikely—consequences of alternative courses of action for specific, real- time foreign policy problems. With limited time and potentially critical consequences, analysts must sort through the uncertainties surrounding the specific problem, providing a best estimate of what is likely to happen, estimating the probability of outcomes different from the best estimate, and assessing contingencies that might lead to alternative outcomes. In each instance, there is an interest to work through the logic of a situation to ascertain what might be done to alter or to facilitate particular outcomes. Keeping the intelligence assessment open to the prospects of a discontinu- ous change is especially important because the past is not a reliable predic- tor of the future (Feder, 2002; Fingar, this volume, Chapter 1). The analyst’s task is daunting. Every case is fraught with unique fea- tures, the time for examining each case is limited, and the potential always exists for deleterious consequences if the analysis proves incorrect. Expert knowledge is the sensible starting place for understanding any specific case, but area or problem expertise should not be the only means of analyz- ing important, complex problems (Tetlock, 2005). Such expertise can be complemented by reliance on well-tested, rigorous methods of analysis. Such methods can provide an independent perspective that informs and stimulates debate. I examine how game theory reasoning, combined with empirical, mostly quantitative, analysis, can help inform foreign policy analysis by (1) foster- ing reliable predictions about the likelihood of alternative outcomes and by assessing how alternative tactics and strategies might improve the expected 57

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58 INTELLIGENCE ANALYSIS: FOUNDATIONS results; (2) identifying conceptual categories that can be combined to reflect the essence of most foreign policy problems, providing an organizational tool for recognizing commonalities across seemingly disparate events; and (3) highlighting some important ways in which inferences about specific events can go awry because of unstated assumptions or logical leaps from past observations to the current, specific situation. This chapter proceeds as follows: First it explains briefly what game theory is and how it differs from some methods that seem to be closely related. The chapter then builds toward the ultimate goal: reliable means to predict and engineer policy outcomes. To do so, the chapter discusses the generic classes of constraints commonly designed into different game theory models, especially conceptual constraints that can help inform and organize approaches to foreign policy problems. It then turns to some of the common empirical or research-design challenges that can result in mis- taken inferences and, therefore, unreliable assessments of specific situations. The chapter then reviews the record of game theory models as a means to facilitate the prediction and engineering of outcomes, especially in the intelligence/national security setting. Following that discussion, some of the important limitations of game theory are reviewed, touching on alternative methods that may be better suited for certain types of problems. I close with a concluding section. WHAT IS gAME THEORY? Game theory is a body of reasoning, grounded in mathematics but readily understood intuitively as a reflection of how people may behave, particularly in situations that involve high stakes for them. It is part of a family of theories that assume people are rational, meaning that they do what they believe (perhaps mistakenly) is in their best interest. Models of decision making such as prospect theory (Kahneman and Tversky, 1984; Kahneman and Miller, 1986) and operations research (Kaplan, this volume, Chapter 2), for instance, examine rational choices in situations in which people confront constraints such as limited time, limited budget, incomplete or uncertain information, or other structural impediments. Game theory models examine choices under these constraints while also specifically attending to strategic interaction in which decision makers select their actions, taking into account expectations about how others will respond to them. Although all games have shared characteristics, including points at which choices need to be made—terminal points reflecting the possible outcomes of a game and player pay-offs or expected pay-offs—they also vary in other features. In some models, players move sequentially; in others, simultaneously. The two ways of ordering moves often are blended together

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59 APPLICATIONS OF GAME THEORY by recognizing that uncertainty can be captured partially by treating moves as simultaneous. Thus, games may be played under conditions of uncer- tainty. Although they must have at least two players, they can have any number above that. Games may be single-shot, repeated (meaning the same players interact over the same set of pay-offs more than once), or iterated (meaning that the same players interact more than once with the pay-offs varying across iterations). The various ways in which the features of a game combine can provide a framework for interpreting specific foreign policy matters in a broad setting whose logic has been carefully explored. I will try to illustrate that with examples in the next section. Games are solved by looking ahead, anticipating (rational) responses by others to each action a player can take, and working backward to for- mulate a plan of action—a strategy—for the best way to reply to each of the actions others could choose. This is, of course, exactly what players of games like chess or checkers do. They try to anticipate how others will respond to different moves and they pick the move they believe is best for them given their expectations about how their rivals will play the game. In that sense, all game theory models compel us to think about counterfac- tual circumstances and not just about what actually happens (Tetlock and Belkin, 1996; Fearon, 1991). Just observing what “really” happened, while ignoring counterfactual actions (actions off-the-equilibrium-path in game theory jargon), can result in misleading inferences about both the process leading to an outcome and the content of the outcome itself (Fingar, this volume, Chapter 1). Game theory diminishes this risk. The solution to any game ensures insight both into what really happened (the actions taken and therefore on the equilib- rium path) and why alternative actions were not taken.1 Why, for instance, did President Kennedy choose a naval blockade as a key response to the introduction of long-range ballistic missiles into Cuba by the former Soviet Union? He certainly understood that the blockade could not remove the missiles already in Cuba. He also understood that other military means might have had a better chance of either destroying the missiles or compel- ling the Soviets to withdraw them. But the expected cost–benefit assessment from alternative approaches such as a tactical airstrike against the missile installations or an invasion of Cuba to overthrow the Castro regime (all moves considered and not made) were inferior to the expected net gains 1 Games are solved by finding Nash equilibrium strategies. A strategy is a complete plan of action covering every contingency that can arise within the game. A Nash equilibrium is defined as a set of strategies such that no player has a unilateral incentive to switch to some other plan of action. Equilibria describe the path of play leading to an outcome and also the actions not taken; that is, placed off the equilibrium path, because they are not best replies for some player.

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60 INTELLIGENCE ANALYSIS: FOUNDATIONS from the chosen approach. That is, these other approaches were placed off the equilibrium path because they were deemed inferior in expected results. Games can have multiple equilibria. A change from one equilibrium outcome to another can appear as a discontinuity. Because different equi- libria typically result from having crossed a threshold value on one or more predictor variables, seemingly discontinuous outcomes—a switch from one plan of action to another when the values on the explanatory variables no longer support a previous strategy—can follow after a long period of smooth, continuous changes in the values of those variables. The collapse of the former Soviet Union illustrates this point. Some look at the demise of the Former Soviet Union as an unpredict- able, discontinuous event (Gaddis, 1992). Others, as reported in the Soviet newspaper, Izvestiya,2 examining strategic decision making under economic and political constraints, predicted that the Soviet Union was steadily approaching a cut-point between alternative outcomes. On one side—the cold war years—the Soviet economy was running down, but it was not yet bad enough to jeopardize the leadership’s hold on power. On the other side of the cut-point, a small further decline in the economy led to insufficient resources to sustain the system and so called for radical internal change. Thus, from a game theory perspective, the discontinuous outcome was the predictable consequence of a continuous, long-term process of economic erosion and shifting political incentives. Of course, game theory is not the only method for evaluating change. Statistical methods, for instance, are at least as well suited for trend analy- sis. Likewise, game theory is not the only mode of reasoning appropriate for studying problems related to questions such as regime stability, the efficacy of carrots and sticks in extracting policy concessions, or the propensity for some issues to be resolved through negotiation and for others to escalate to violence. Political psychology is rich with individual-level assessments of decisions affecting fundamental national security matters (McDermott, 2007). Organizational theory and social forces (see this volume’s Spellman, Chapter 6; Tinsley, Chapter 9; and Zegart, Chapter 13) help us to under- stand how decisions are shaped by and shape group dynamics (see Hastie, this volume, Chapter 8). But equally hard to escape is the fact that strategic interaction—the intentional maneuvering between contending parties—is central to international affairs and is at the heart of many problems con- fronted by intelligence analysts. Indeed, game theory provides ways to integrate much of the important knowledge derived from structural, organizational, behavioral, and psy- chological theories. Structure is a central element in games of sequential decision making in which choices are constrained by the situation in which 2 April 3, 1995, based on the Central Intelligence Agency’s Foreign Broadcast Information Service’s translation.

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61 APPLICATIONS OF GAME THEORY decision makers find themselves (Acemoglu and Robinson, 2005; Bueno de Mesquita et al., 2003; North et al., 2009; Shepsle, 1979; Hastie, this volume, Chapter 8). Those situations, or organizational structures, in turn, can be traced back to the strategic interplay among an organization’s found- ers, leaders, and members (Morrow, 1994; Downs et al., 1996). Beyond structural constraints, games also address individual decision-maker char- acteristics such as their preferences, orientation toward risk taking, and beliefs. Although preferences and risk orientations are taken as psycho- logical features of the individual, beliefs may be a combination of personal predilections and experience. They are assumed to be sustained as long as there is no substantial evidence to contradict them, but they are modified in accordance with Bayes’ rule (Kaplan, this volume, Chapter 2) when new information proves to be inconsistent with prior beliefs. Of course, game theory recognizes that many decisions must be made with uncertainty about virtually any and every aspect of a situation. No single game or model fits all international affairs. Rather, classes of games reflect particular combinations of constraints that act as potential impediments to any player getting what it wants. Therefore, the intelligence analyst, whether formally trained in game theory or not, can benefit from working out the strategic implications of different mixes of individual and structural constraints that are crucial to any given situation. By doing so, the analyst can gain an upper hand in thinking about the strategic lay of the land and, if the right tools are available for more formal, rigorous analysis, can also employ those tools to help work through the complex array of plausible (and implausible) developments and potential ways to alter them. I now turn to these crucial classes of constraints. CATEgORIZINg CONSTRAINTS ON FOREIgN POLICY ACTIONS In thinking about national security problems, five constraints draw our attention to features of different games that can help illuminate the analysis of national security issues. These constraints are: (1) Uncertainty; (2) Risks; (3) Distribution of costs and benefits; (4) Coordination; and, in the case of recurring situations, (5) Patience. Let’s consider each constraint, identifying the essential elements and providing illustrative examples. Uncertainty Uncertainty is a nearly ever-present concern. Information is hard to come by about the intentions of rivals, their capability to implement their intentions, their resolve to do so at different levels of costs borne by them (whether inflicted by others or self-imposed), and their beliefs about U.S. intentions, capabilities, and resolve. Uncertainty creates the opportunity

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62 INTELLIGENCE ANALYSIS: FOUNDATIONS for rivals to bluff about their true qualities, sometimes with the objective of making analysts or decision makers believe they are more hawkish—or more dovish—than they actually are. As in poker and many other games, a successful bluff can produce bigger rewards than could be attained if all information were open for everyone to see and evaluate. But, of course, bluffs are risky. They can also lead to undesired outcomes. Game theory looks at uncertainty two ways. One source of uncertainty arises because of random shocks to a situation. These random developments can change player expectations and, therefore, the actions they choose.3 Key figures might die unexpectedly (Jones and Olken, 2009) or some event, such as a natural disaster (Bommer, 1985; Brancati, 2007), might alter the focus of decision makers or the ease with which rivals can organize. Mod- els that allow inputs to be randomly altered (i.e., to experience stochastic shocks) provide a way to think about unanticipated, random events that might alter developments and probe the robustness of alternative outcomes (Bueno de Mesquita, 1998). Uncertainty also arises in the form of not knowing some critical piece of information about a player, such as his or her preferences, capabilities, or expectations. These situations are sometimes described as circumstances in which players do not know what game they are playing. This form of uncertainty—about player types in game theory jargon—is dealt with by attaching probabilities to player types and having nature—a nonstrategic actor—draw the player types in accordance with the explicitly assumed probability distribution.4 Let me illustrate this approach to uncertainty while also illustrating the principle that uncertainty reduction, contrary to intuition, does not necessarily increase the odds of finding a cooperative solution to a conflict-prone problem. Indeed, reducing uncertainty often increases the chances of resolving a dispute cooperatively by making clear to both sides how events are likely to unfold. Less uncertainty can help the side that sees it will pay a heavy cost find a negotiated agreement that leaves it better off than it expected to be by resisting. The improvement in welfare arises because concessions now 3 Modelers often refer to developments or circumstances that are not determined within the logic of the situation, but nevertheless are relevant to shaping choices as exogenous. Weather conditions, for example, are exogenous. However, a decision to initiate a military action or to hold back is not exogenous; it is, in game theory jargon, endogenous because there is a choice to be made about when to attack given expectations about weather, the exogenous factor. I return to this important distinction later. 4 Uncertainty is addressed by converting incomplete information (not knowing player pay- offs or expectations at the end-points of the game) into imperfect information (not knowing the prior history of play) by creating player types and a subjective probability distribution over the types (Harsanyi, 1967–1968). In this way, players do not know where in the game they are when prior choices are consistent with the interests of different types, but subsequent actions will follow different strategic paths depending on the types.

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63 APPLICATIONS OF GAME THEORY are partially compensated by the transaction costs avoided later (Fearon, 1995). But sometimes reducing uncertainty increases the risk of conflict escalation instead of defusing it. Consider this highly simplified example of potential interactions between a government and terrorists.5 Some governments—the U.S., British, and Israeli governments are nota- ble examples—have declaratory policies that they will not negotiate with terrorists. Imagine a disgruntled, relatively weak group that feels ill treated and would like the government to be more responsive to its perceived grievances. Its members are uncertain whether the government will take them seriously if they come forward to try to negotiate a resolution of their grievances. Some group members propose that the government will pay more attention if the group launches an act of terrorism to raise awareness of their cause. These members note that this worked for the Palestinian Liberation Organization, the Irish Republican Army, and others. Although the group is divided on this question, the hardliners prevail. Following the terrorist action, the group debates whether to now come forward and seek concessions from the government in exchange for laying down their arms and eschewing future violence. Imagine that on average the group values a negotiated agreement with the government more than engaging in another attention-getting act of terrorism, but the members agree that such an act would be better than coming forward, seeking to make a deal only to find their group ignored or even suppressed. For arguments sake, let’s say that they value a prospective negotiated deal at 100, being ignored or suppressed at 0, and another act of attention-getting terrorism at 40. If the government has no declaratory policy about negotiating with terrorists, then the group is likely to be uncertain about how the govern- ment will respond if they now come forward-seeking concessions. They do not know the government’s type: suppressor or compromiser. If the group thinks the chance that the government is the compromiser type is 0.5 and the chance that it is the suppressor type is also 0.5 (so that they have maximum uncertainty about the likely response by the government), then their expected value from coming forward, trying to negotiate, is 0.5(100) + 0.5(0) = 50. Because this is better than the value (40) they attach to a second act of terrorism, they take their chances and try to negotiate. Perhaps they are lucky and the government turns out to be the compromiser type that grants some concessions in exchange for the group disarming and perhaps they are unlucky, with the government being the suppressor type. Although uncertainty about the government’s type might result in the 5 For more nuanced game-theoretic treatments of terrorism, see Bueno de Mesquita (2005, 2008); Bueno de Mesquita and Dickson (2007); Kydd and Walter (2002); Lapan and Sandler (1988, 1993); and Rosendorff and Sandler (2004).

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64 INTELLIGENCE ANALYSIS: FOUNDATIONS opportunity for negotiation, consider what happens if the government reduces uncertainty about its true type. Suppose the government has a declaratory policy that it will never negotiate with terrorists. Because reneg- ing on a public declaration of this sort can be costly for democratic leaders, jeopardizing their chances of reelection and encouraging future adversar- ies to see them as weak or lacking commitment to their stated intentions (Fearon, 1994; Smith, 1998; Schultz, 1998), the declaratory policy increases confidence in the belief that the government is the type that will not negoti- ate with terrorists. That is, the declaratory policy has reduced—if not com- pletely eliminated—uncertainty about how the government will respond to a request for negotiations by the alienated group. Suppose the group now places the odds that the government is the suppressor type at 0.7 instead of 0.5. With reduced uncertainty about the government’s type, the group’s expected value from seeking negotiations now is 0.3(100) + 0.7(0) = 30. A second act of terrorism is valued at 40 so, with uncertainty reduced, the prospect of more terrorism increases.6 Uncertainty generally increases the number of possible equilibrium out- comes in strategic settings. Even though players do their best to digest what- ever information comes their way, what they believe and what is actually true can deviate, resulting, as in the terrorist example, in an outcome that is not optimal from anyone’s point of view. This reminds us that rational, strategic actors can, nevertheless, end up with bad outcomes. Risks Whereas uncertainty is about not knowing an important piece of information—say whether a government will pursue negotiations with terrorists—risk is concerned with the probability of alternative results, given different choices of action. In making a bet that I will roll a 6-sided die and come up with a 6, there is no uncertainty about the probability of a 6 being the outcome, although the bet is certainly risky. If the die is fair, then there is a 1/6 chance of rolling a 6 and winning the bet. Plus, there is a 5/6 chance of losing: Risky choices can, of course, lead to bad outcomes. Different people respond to known risks differently. Some are reluctant to take risks, while others attach so much value to a successful outcome rel- ative to the low value they attach to failure that they favor gambling for the big win over even a fairly valued sure outcome. Estimating the willingness 6 This is a stylized example to make clear how uncertainty reduction can exacerbate rather than diminish tensions. Of course, a fuller analysis would need to take into account the reputational effects of alternative courses of action, the elasticity of demand to be a terror- ist conditional on changes in the expectation that the government will inflict costs on such groups, the credibility of the government’s commitment to provide policy concessions, and the credibility of the terrorist group’s promise to disarm, as well as many other considerations.

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65 APPLICATIONS OF GAME THEORY to gamble—a player’s risk aversion or risk acceptance—in a foreign policy context is a difficult, iffy business, but it also is an important undertaking if we are to design and solve strategic problems that can be of practical use to intelligence analysts (Bueno de Mesquita, 1985; Morrow, 1987; O’Neill, 2001; see also Fischhoff, this volume, Chapter 10). Risk-proneness draws attention to how risks, weighted by the value or utility attached to alternative outcomes, shape expected pay-offs. Risk by itself is central to all rational choice models of decision making (Kahneman and Tversky, 1984; Kahneman and Miller, 1986; Riker, 1996; McDermott, 1998; see also Kaplan, this volume, Chapter 2). The fall of Iran’s Shah provides insight into how attentiveness to actuarial risks and their strategic implications might have informed analysis about regime change. Nondemocratic leaders who survive in office past approximately 1 or 2 years experience a significant year-to-year decline in the risk of being ousted (Bueno de Mesquita et al., 2003; Egorov and Sonin, 2005), all else being equal. That does not tend to be true for democrats. So, looked at from this angle, it is easy to see why analysts and decision makers would have been taken by surprise when the Shah was deposed in 1979, 38 years into his rise to power and 22 years after his coronation. However, all things are not equal. Mortality, for instance, cuts against the general trend of long-term political survival. The longer a leader is in power, the older the leader gets, and, therefore, the greater the risk of contracting a serious or even terminal illness. Analyses of political survival indicate that nondemocratic leaders known to be suffering from a terminal illness—as the Shah was—are par- ticularly vulnerable to being deposed by a coup or revolution, apparently because their supporters, especially in the military, can no longer count on them to deliver a flow of largesse, so they factionalize as they look for a new patron to take care of them (Bueno de Mesquita et al., 2003; Goemans, 2008). The risk of revolution when a dictator is dying is likely also to be increased by the propensity of such leaders to surround themselves with relatively incompetent advisors—that is, advisors who are not likely to be good candidates to become rivals of the incumbent (Sonin and Egorov, 2005). Of course, autocrats understand what drives the risk of deposition, so they commonly try to keep their illnesses secret. But when the best medi- cal care can be had only outside their country, as was true for the Shah (and Mobutu Sese Seko in then-Zaire and many others), then there is little they can do to avoid the risk that the illness becomes common knowledge. The Shah’s illness was known for some time before he was overthrown. The risk to the stability of his regime was, therefore, something that could have been anticipated and calculated. Of course, terminal illness does not guarantee a revolution, but it certainly raises the odds.

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66 INTELLIGENCE ANALYSIS: FOUNDATIONS Distribution of Costs and Benefits Distributional conflicts arise over the relative costs and benefits associ- ated with different outcomes of a game. For example, wars are sometimes fought to gain wealth or territory (Huth, 1996; Vasquez, 2009), or, in the case of certain regime types, to impose policies on recalcitrant adversar- ies (Bueno de Mesquita et al., 2003; Bercovitch and Lutmar, 2010) or to spread values (O’Donnell et al., 1986; Karl, 1990). Each of these factors involves distributional issues between rivals, so they can be assessed in a game-theoretic framework. The combination of uncertainty and distributional issues creates com- plex situations in which rivals have incentives to bluff in an effort to steer action toward their desired outcome. Thus, a player might claim to be more resolved to get its way than it truly is. It might try to signal this resolve by making verbal threats or by taking visibly costly actions, such as mobilizing its military, in the hope that its words or actions will convince others to sac- rifice what they want in order to avoid threatened costs. Thus, uncertainty about costs and benefits not only can provoke bluffs, but also can provide a means to reduce the odds of being taken in by a bluff. Consider the difference between bluffs that are costly to make and bluffs that cost nothing. Threats intended to deter an adversary can be purely verbal cheap talk (private communication, for instance, that “there will be dire consequences if . . . ”) or they can be accompanied by a costly signal, such as the visible mobilization of armed forces (or a public dec- laration that “there will be dire consequences if . . . ”, especially if made by a politician up for reelection [Fearon, 1994; Smith, 1998]).7 A private declaration of resolve, for instance, to deter Iran from building a nuclear weapon, would not be the same as public statements or costly actions demonstrating such resoluteness by, for example, conducting military flights over Iran’s nuclear sites or massing troops on Iran’s border. Talk is cheap unless the declaration is accompanied by self-imposed high costs. Costly actions increase the threatening party’s own costs with- out guaranteeing that the threatening party will receive offsetting gains. Therefore, the higher the self-imposed costs, the more likely it is that the threatened action is serious and not a mere bluff (Banks and Sobel, 1987). It is noteworthy that the United States makes only vague statements about 7 Cheap talk refers to signals (communication, statements) between players that do not in- fluence the costs and benefits; that is, the pay-offs, to the players in the game. In the unusual foreign policy case of pure coordination, cheap-talk signals are taken as meaningful because players have no incentive to bluff or deceive each other (Crawford and Sobel, 1982; Spence, 1973; Sartori, 2005). In situations not only involving coordination, such as when there are disagreements about the allocation of scarce resources, cheap-talk statements are equivalent to babbling. They convey no information.

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67 APPLICATIONS OF GAME THEORY not tolerating an Iranian nuclear bomb, but undertakes actions—such as economic sanctions—that inflict small costs on American voters and, there- fore, on American politicians. The focus on sanctions is more often on the costs to the target than the costs borne by the threatening party. This raises a closely associated distribu- tional question in strategic environments that lead to sanctions. A perennial question is whether sanctions successfully alter the likely outcome of a game and, therefore, the distribution of costs and benefits across players. Often they do not (Hufbauer et al., 2007; Martin, 1993; Smith, 1996a). When the self-inflicted costs are small—as is true for the costs borne by the United States in sanctioning Iran—then the adversary is relatively unlikely to believe that the sanctioner is serious about altering the outcome of the situation. Furthermore, if the costs to some sanctioning parties get to be significant, then it is likely that they will try to renegotiate the terms of their agree- ment to sanction to avoid continued costs (Abreu et al., 1993). In addition, despite widespread advocacy for imposing sanctions to redistribute costs and benefits in many difficult foreign policy situations, both logic and evidence show that sanctions are more likely to be effective at the threat stage than at the implementation stage. This is because they are only likely to need to be implemented if their target has already concluded that the prospective costs of the sanctions are smaller than the prospective costs of granting the conces- sions that would avoid sanctions (Smith, 1996a; Drezner, 1999). Therefore, the threat of sanctions can be a powerful tool for altering the outcome of some disputes, but their implementation rarely is. Finally, distribution issues often reveal commitment problems. Some- times disputants make promises (e.g., cease-fire agreements), but the mere existence of a cheap-talk promise reveals nothing about what action should be expected. The Taliban, for instance, promised not to disrupt the 2009 Afghan election, yet reneged on that promise. Why? Because low turnout could help advance the Taliban’s interests. Likewise, repeated efforts to forge land-for-peace or peace-for-land deals between Israel and the Palestin- ian Authority suffer from commitment problems associated with the over- riding difference in distributional interests of the two sides. Promising peace for land runs into the problem that once land concessions are granted, they are costly to withdraw. So, once land concessions are implemented, the other side has incentives to say the concession is not sufficient to warrant peace (Powell, 1999). Peace for land has exactly the same problem. Once militants disarm in expectation of getting land concessions, the Israelis have little incentive to carry out their part of the bargain because the militants have given up their threat power. Distributional issues often prompt these sorts of commitment issues in foreign affairs. Analysis that treats promises as meaningful, even when carrying them out is contrary to their maker’s interests, is bound to lead to overly optimistic conclusions.

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72 INTELLIGENCE ANALYSIS: FOUNDATIONS to come to their ally’s defense (Sabrosky, 1980; Leeds et al., 2000, 2002).10 Some infer from the high percentage of alliance partners who do not fight for their partner that treaty obligations are not a meaningful signal of a shared commitment to coordinate under costly conditions. Notice, however, that this inference is drawn by looking at the response of the alliance part- ner “if the ally is attacked.” That, as we will see, is a problematic qualifier if we want to evaluate alliance reliability. Consider the following mind experiment. Suppose the leader of nation A has a rival, an enemy state called B. That rival has an ally, C. Countries like C frequently do not assist B following an attack by A. We know that information from data analyses whose dependent variable asks whether allied states got help from their partners when attacked. But such analyses do not ask whether an attack took place; attack is taken as given. Yet the underlying question of interest is the reliability of alliance commitments. By ignoring cases in which nothing happened—no attack took place—an empirically incorrect inference is drawn because of improper case selection. The reported pattern of behavior is insufficient to infer that alliances are unreliable. In fact, the observation is exactly what we should expect if alliance commitments are credible. Consider the following two cases in which A is equally motivated to extract something of value from B and concludes that the valued good can only be gotten by attacking B. In case 1, A attacks B, and in case 2, A does not attack B. To keep matters simple, I assume A believes it can defeat B and gain a benefit that exceeds the anticipated costs of a fight just with B. Suppose, however, that A does not believe the benefits warrant the expected costs of a fight against both B and C. Then, if A believes C’s alliance commitment to B is reliable, A does not attack B and we do not include the ongoing peaceful interaction between A and B in our data analysis. If A believes the alliance is unreli- able, A attacks B and the case is included in the data analysis. Naturally, some of the time A’s beliefs will be mistaken because of uncertainty about a state’s true degree of commitment (Gartzke, 1999; Coletta and Gartzke, 2003). However, in general we expect that A’s beliefs will be consistent with the subsequent behavior of C because the cost to A of getting this wrong is likely to be high (Huth, 1988; Huth and Russett, 1984; Wu, 1990). By examining only cases of attack, we fail to test alliance reliability properly. A focus on strategic interaction instructs us to anticipate that we should expect that the applicable alliances will generally prove to be unreli- able if an attack has taken place. A, after all, has already taken into account 10 Nearly five times as many alliance partners become war participants following an attack as do nonallied states (Siverson and King, 1980), so clearly alignment helps predict choices if an attack happens, but, as we will see, that is not particularly informative about the general reliability of alliance commitments.

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73 APPLICATIONS OF GAME THEORY the anticipated reliability of C’s commitment as part of A’s strategic deci- sion making about whether to attack B. If A believes C will assist B, then A chooses not to attack, making C’s reliability an unobserved state of affairs because A places “attack” off the equilibrium path. The empirical expecta- tion, then, is that the most reliable alliances do not get tested because they succeed in deterring attacks, while the relatively less reliable alliances are more likely to be tested and, as expected, prove wanting. The evidence sup- ports the selection argument regarding alliance reliability (Smith, 1996b). Dominant arguments among international relations scholars and prac- titioners about the effects of bipolarity, multipolarity, and the balance of power on stability suffer from just such theoretical selection effects and empirical selection bias, as does much writing on the rise or decline of great powers. A careful examination of the arguments for why bipolar or multipolar systems or balanced or imbalanced power systems are likely to promote stability shows, for instance, that the logic behind these arguments depends on assumptions that lead to hypotheses not supported by studies without selection bias (Bueno de Mesquita, 2009; Kim and Morrow, 1992; Niou et al., 1989; Powell, 1999; Vasquez, 1997). Endogenous Choice Selection bias in sampling often results from a failure to think through how the strategic setting creates values on key explanatory variables that, in turn, lead to strategic selection of actions. Statistical analysis runs into this failure because it generally assumes that the values taken by indepen- dent variables are exogenous; that is, are determined outside the strategic setting rather than shaped by it.11 In strategic settings—and most foreign policy problems involve a substantial element of strategic interplay between contending sides—the assumption that the values of the explanatory vari- ables do not depend on expectations about how they will shape outcomes is problematic. When choices are made strategically, they are forward look- ing. One course of action is chosen over others because it is expected to have better consequences down the road. In this sense, attending to reverse causality is of fundamental importance—looking ahead to work out what the best action is now. One simple example is to consider whether Christ- mas tree sales cause Christmas or the anticipation of Christmas causes tree sales. Behind this example lies an important consideration for policy 11 Theexception to this statement involves the application of Bayesian statistical estimation techniques. These are rarely found in studies of foreign affairs. For two excellent examples of the use of such methods, each motivated by game theory’s strategic reasoning, see Smith (1999) and Ward et al. (2007).

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74 INTELLIGENCE ANALYSIS: FOUNDATIONS analysis. Let me illustrate that consideration with a discussion of arms races and their relation to war. Many contend that arms races cause war (Richardson, 1960; Wal- lace, 1982; Diehl and Crescenzi, 1998; Gibler et al., 2005). This belief contributes to efforts to pursue arms control agreements in the expectation of improving the prospects of peace. The standard account of how arms races cause war builds on stimulus-response, nonstrategic explanations of arms racing. The claim is that when a country builds up its arms, it makes its adversaries fear that their security is at risk. In response, they build up their own arms to defend themselves. The other side looks at that build- up—seeing their own as purely defensive—and responds by developing even more and better weapons to protect themselves, fearing that the other side intends to take advantage or even attack them. Eventually, so the argument goes, the arms race (inexplicably) spirals out of control and war starts. In support of this contention, evidence is adduced that wars are pre- ceded by arms races. The arms build-up is taken as exogenous, as inde- pendent of the threat or expectation of war. Here we have correlation masquerading as causation, with little regard to the underlying strategic environment. After all, the most basic economics teaches us that when the cost of anything goes up, holding quality constant, we buy less, not more of it. Arms build-ups increase destructive power and, therefore, the expected cost of war. By raising the expected cost of war while leaving the value of war’s benefits unaltered, arms racing should reduce, not increase, the incidence of war although, if a war occurs, it will be costlier because of the arms build-up. Just about every war has been preceded by a build-up in weapons, but then many wars are also avoided by the deterrent impact of an arms build- up (Powell, 1990, 1999; Bueno de Mesquita and Riker, 1982). Much of the empirical literature on arms races results in poor sampling of cases because of a failure to understand that arms acquisition is endogenous to the expectation of war. That is, the fear of vulnerability to an adversary causes arms races, rather than the decision to acquire arms being the cause of war (Altfeld, 1983; Powell, 1990, 1999). Thus, the idea of forward-looking, endogenous choice confounds assessments that treat the value on explana- tory variables as being independent of expectations about future events. PREDICTION OF FUTURE EVENTS The discussion of strategic constraints and the empirical challenges they create should encourage testing hypotheses by observing past patterns (whether through case studies or statistically in large-N studies) and then projecting the expectations they imply on out-of-sample cases. That is the problem faced by intelligence analysts. They know what happened in

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75 APPLICATIONS OF GAME THEORY the past and they must figure out which past patterns are germane to the problem they confront at the moment, a problem whose resolution is still unknown. The intelligence analyst’s problem is perhaps the most challeng- ing for any theory. Prediction (forecasting) is demanding exactly because the researcher cannot fit arguments to unknown results. This is a fundamental difference between real-time prediction and so-called post-diction. Not surprisingly, few theories of international relations are routinely exposed to the demands of real-time prediction. Among quantitative efforts to predict national security problems, a few stand out for their success and the ease with which they can be applied in real-time. Artificial neural network models, for instance, are a statisti- cal means to “train” their algorithm to new cases by discerning patterns among variables based on prior observations, then updating the weights of variables as new observations are added, using the “training” to anticipate the next out-of-sample case. Beck et al. (2000) and King and Zeng (2001) have used such methods to predict patterns of conflict initiation and of state failure with considerable success. Other quantitative, but not statistical, approaches to foreign policy problems have also proven effective in predicting the dynamics and the outcomes of out-of-sample events. Some applied game theory models, for instance, have been used to evaluate national security problems and have even found use among some intelligence analysts. Statistical assessments, including regression, maximum likelihood, artificial neural network mod- els, and others, are especially valuable when the past is a good predictor of the future. Applied game theory models provide a useful alternative to more conventional statistical analyses in that applied games have greater case-specific qualities. They also are equally helpful in looking at ongoing situations and cases involving the prospect of discontinuity. Furthermore, they highlight sources of selection effects, compel attentiveness to endog- enous choices, and keep the derivation of hypotheses—done through formal logic—independent of the data used to evaluate them. Game theory also provides explicit means of modeling how uncertainty alters the strategic interplay among decision makers and provides a means—through Bayes’ rule—for taking learning into account. Other methods address many of these items as well, but to my knowledge game theory modeling is the only approach structured to draw explicit analytic attention to all of them. A final reason for focusing attention on game theoretic approaches to international relations is their track record when applied to national secu- rity matters. Indeed, Stanley Feder (2002), a former Central Intelligence Agency (CIA) analyst and national intelligence officer, emphasizes the vir- tues that strategic models bring to the job of intelligence analysts precisely because such models help anticipate divergence from past patterns. Feder reports that at least one such model that he tested more than 1,200 times

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76 INTELLIGENCE ANALYSIS: FOUNDATIONS during his tenure at the CIA produced accurate results 90 percent of the time and provided a means to extrapolate to significant implications about matters such as regime stability, leadership change, and responsiveness to alternative approaches to a given problem (Feder, 1995, 2002). Others report similar reliability when reviewing academic publications concerning the same applied game theory models (Ray and Russett, 1996). Feder contends that the intelligence community would benefit from greater use of such models (for ways to evaluate this expectation, see Tetlock and Mellers, this volume, Chapter 11). He argues that these mod- els do not get greater use because analysts tend to think of quantitative or mathematical approaches as the domain of methodologists rather than as part of their domain of country-specific or problem-specific analysis. For- tunately, analysts do not need to be methodologists or game theorists to capitalize on the insights that can be gained from thinking about problems in a strategic vein. They can combine their deep understanding of history, culture, and idiosyncratic factors impinging on any case with the case- oriented insights of applied game theory models, rendering their analysis more complete and transparent. LIMITATIONS Of course, a cultural divide between humanistic and social science approaches to intelligence analysis—as highlighted by Feder (2002)—is not the only factor that restricts the adoption of statistical or game theoretic methods by the intelligence community. Humanistic modes—examinations of history, culture, and local conditions—provide important insights into intelligence problems. When coupled with social science methods, the two together have demonstrated much more insight than either alone (Feder, 1995, 2002). We should not lose sight of the fact that humanistic modes of analysis face limitations of their own. They lack analytic transpar- ency; different subject or area experts often draw different inferences when confronted with the same facts; and tools for evaluating accuracy are inaccurate either with regard to outcomes or the process leading to them. Likewise, we must also be explicit about the limitations of more social- science–oriented methods. Game theory forecasting methodology used to evaluate political deci- sions, as reviewed by Feder (1995, 2002), Ray and Russett (1996), and others (e.g., Thomson et al., 2006; Schneider et al., 2010), can combine the benefits of detailed case assessment while exploiting the advantages of broad hypothesis testing through the application of the same model to numerous individual cases. But game theory applications make strong assumptions about information and people.

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77 APPLICATIONS OF GAME THEORY Games require that at least some critical element of information must be common knowledge; that is, at least some information must be known to each player, who must know that each other player knows that informa- tion, and each player must know that each other player knows that each player knows the information and so forth. Although there is considerable ongoing research to escape the common knowledge conundrum—especially when it comes to assumptions about the probability that players hold this or that belief about others—standard game theory models still have not overcome the common knowledge constraint. Some argue that this require- ment cannot be overcome in a foreign policy context (Fey and Ramsay, 2007). Additionally, the path to outcomes in game theory models is well defined and (perhaps overly) precise. The path to outcomes in the real world tends to be fairly noisy, involving more randomness and often taking longer, with many more steps, than in formal game theory models. This has stimulated several complementary technologies. One approach focuses attention on the costs and benefits of searching for the best action to take. These models, known as “satisficing” models—in which players choose the first adequate approach to a problem that they identify—and other models in which play- ers have bounded, that is, limited rationality, are two modifications to stan- dard game theory models designed to cope with potentially overly defined outcome paths (Simon, 1957; Sargent, 1994; Byron, 2004). But in doing so, these perspectives introduce their own problems. They increase the number of equilibria and suggest paths to outcomes that may be no closer—and might even be less close—to the choices of actual decision makers than is true in standard game theory modeling. Indeed, evolutionary models—that incorporate various forms of short-sighted behavior—stabilize at a Nash equilibrium outcome of a more standard game designed to capture the strategic setting.12 Yet evolutionary models can arrive at the evolutionarily stable equilibrium from a nearly infinite number of paths, implying that the process of decision making leading to outcomes is unpredictable. If that is true, then outcome predictions may still be reliable, but predictions about process are unlikely to be. The evidence from intelligence applications of game theory models, however, challenges this inference. Standard games 12 Evolutionary game theory builds on the insights of evolution in biology. Essentially, evolutionary models assume that players continue a strategy or course of action as long as it produces good results for them, switching to a different strategy when their behavior proves excessively costly. Nash equilibrium is the fundamental concept for solving games. In game theory, players have strategies, defined as a complete plan of action for every contingency that could arise in the game. A Nash equilibrium is a set of player strategies in which no player has a unilateral incentive to deviate from his or her strategy.

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78 INTELLIGENCE ANALYSIS: FOUNDATIONS seem to provide insight into the choice process as well as into the outcome of events (Feder, 1995, 2002).13 Although no rational choice models assume that decision makers have perfect foresight or that decision makers explore all possible avenues of action, they do make strong assumptions about how problems are solved. Because the actors in these models are trying to do what is best for them, they are assumed to play skillfully and without emotion. The game theo- retic decision maker is cold, calculating, and self-interested. Of course not everyone behaves that way all of the time so, as with any method, it is prudent to view the results of a game as information to be taken as one of several inputs. In forming a well-rounded assessment of a problem, it is also important to examine the insights from many authors in this volume, as follows: from psychology (see this volume’s Spellman, Chapter 6, and Tinsley, Chapter 9), organizational theory (see this volume’s Kozlowski, Chapter 12, and Zegart, Chapter 13), group dynamics (Hastie, this volume, Chapter 8), and history and culture (Skinner, Chapter 5). But at the same time, we should not overstate the limitations that arise from discounting factors such as emotion. After all, Feder (1995, 2002), Ray and Russett (1996), and numerous other independent auditors of game theoretic results about national security matters all conclude that some applied models prove highly reliable, hitting, as Feder puts it, “the bull’s eye” twice as often as the intelligence analysts whose data were used to estimate variables in the applied models. CONCLUSION International relations and foreign policy problems are readily clustered according to the broad categories of constraints examined by game theory approaches. Recall that these constraints include (1) uncertainty; (2) risk; (3) distributional concerns; (4) coordination; and (5) patience. Attention to these constraints, coupled with a focus on strategic interaction, highlights the ways in which selection effects and endogenous choice shape events and, therefore, how ignoring these factors can result in mistaken inferences. By monitoring which strategic constraints are operative in a situation and how they relate to what is or is not observed, the analyst will have a clearer evaluation of the array of plausible and implausible outcomes. Even done intuitively, the factors highlighted by game theory should help 13 Charles Buffalano, then deputy director of research at the Defense Advanced Research Projects Agency, in private correspondence dated June 12, 1984, reported that “one of the last (and most successful) projects in the political methodologies program was the expected utility theory. . . . The theory is both explanatory and predictive and has been rigorously evaluated through post-diction and in real time. . . . [I]t has the power to predict specific policies, their nuances, and ways in which they might be changed.”

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79 APPLICATIONS OF GAME THEORY diminish the analytic pitfalls that make the intelligence analyst’s job so daunting. The knowledge derived from quantitative and formal methods has been successful in informing intelligence analysis. Many of these methods are relatively easy to learn and apply. In all likelihood when the intelligence community is organized to use these social science methods and when its culture changes to welcome these approaches, then, as suggested by the chapters in this volume, quantitative and formal modeling perspectives applied together, with more qualitative and more humanistic methods, will improve analysis and enhance national security. REFERENCES Abreu, D., D. Pearce, and E. Stacchetti. 1993. Renegotiation and symmetry in repeated games. Journal of Economic Theory 60(2):217–240. Acemoglu, D., and J. A. Robinson. 2005. Economic origins of dictatorship and democracy. New York: Cambridge University Press. Allison, G. T., and P. Zelikow. 1999. Essence of decision: Explaining the Cuban missile crisis, 2nd ed. White Plains, NY: Longman. Altfeld, M. 1983. Arms races? And escalation? International Studies Quarterly 27:225–232. Altfeld, M. F., and B. Bueno de Mesquita. 1979. Choosing sides in wars. International Studies Quarterly 23(March):87–112. Axelrod, R. 1984. The evolution of cooperation. Boston, MA: Basic Books. Banks, J. S., and J. Sobel. 1987. Equilibrium selection in signaling games. Econometrica 55:647–661. Beck, N., G. King, and L. Zeng. 2000. Improving quantitative studies of international conflict. American Political Science Review 94(1):21–36. Bercovitch, J., and C. Lutmar. 2010. Beyond negotiation deadlocks: the importance of media- tion and leadership change. In A. Narlikar, ed., Deadlocks in multilateral settings: Causes and solutions (pp. 232-253). New York: Cambridge University Press Bommer, J. 1985. The politics of disaster—Nicaragua. Disasters 9(4):270–278. Brancati, D. 2007. Political aftershocks: The impact of earthquakes on intrastate conflict. Journal of Conflict Resolution 51(5):715–743. Bueno de Mesquita, B. 1985. The war trap revisited. American Political Science Review 79:156–173. Bueno de Mesquita, B. 1998. The end of the Cold War: Predicting an emergent property. Journal of Conflict Resolution 42(2):131–155. Bueno de Mesquita, B. 2009. Principles of international politics, 4th ed. Washington, DC: CQ Press. Bueno de Mesquita, B., and D. Lalman. 1992. War and reason. New Haven, CT: Yale Uni- versity Press. Bueno de Mesquita, B., and W. H. Riker. 1982. Assessing the merits of selective nuclear pro- liferation. Journal of Conflict Resolution 26(2):283–306. Bueno de Mesquita, E. 2005. Conciliation, counterterrorism, and patterns of terrorist violence. International Organization 59(1):145–176. Bueno de Mesquita, E. 2008. Terrorist factions. Quarterly Journal of Political Science 3(4):399–418.

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