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
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 mistaken 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
by recognizing that uncertainty can be captured partially by treating moves as simultaneous. Thus, games may be played under conditions of uncertainty. 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 formulate 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 counterfactual 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 equilibrium 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 compelling 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
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 equilibria 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 unpredictable, 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 analysis. 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 understand 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 confronted by intelligence analysts.
Indeed, game theory provides ways to integrate much of the important knowledge derived from structural, organizational, behavioral, and psychological theories. Structure is a central element in games of sequential decision making in which choices are constrained by the situation in which
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 founders, leaders, and members (Morrow, 1994; Downs et al., 1996). Beyond structural constraints, games also address individual decision-maker characteristics such as their preferences, orientation toward risk taking, and beliefs. Although preferences and risk orientations are taken as psychological 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 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
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. Models 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
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 notable 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 government 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
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 reneging on a public declaration of this sort can be costly for democratic leaders, jeopardizing their chances of reelection and encouraging future adversaries 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 negotiate with terrorists. That is, the declaratory policy has reduced—if not completely 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 outcomes in strategic settings. Even though players do their best to digest whatever 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.
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 relative 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
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 particularly 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 medical 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.
Distribution of Costs and Benefits
Distributional conflicts arise over the relative costs and benefits associated 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 adversaries (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 complex 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 sacrifice 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 declaration 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 without 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
not tolerating an Iranian nuclear bomb, but undertakes actions—such as economic sanctions—that inflict small costs on American voters and, therefore, 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 distributional 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 agreement 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 concessions 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. Sometimes 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 Palestinian Authority suffer from commitment problems associated with the overriding 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.
An interest in coordinated action arises among players when they want to work toward a common resolution of an issue. For example, whether allies can be counted on to help out in time of war is a question of incentives to coordinate (Altfeld and Bueno de Mesquita, 1979; Siverson and King, 1980; Smith, 1996b; Leeds, 2003).
Although some coordination problems are not complicated by other factors, most are. The rare pure coordination issue, like whether allied tanks should drive on the left or right side of the road in a combat zone, responds well to cheap-talk signals because the parties involved have no incentive to bluff or misrepresent themselves (Calvert, 2006; Crawford and Sobel, 1982; Spence, 1973). Resolution based only on exchanging information does not work if the coordination problem is complicated by differences in distributional preferences.
Interests in coordination—though rarely pure coordination—are widespread in international crises. When disputes involve multiple parties, for instance, adversaries have an interest in building a coalition capable enough to deter or defeat the other side. Coalition formation inherently involves coordination, combined with finding distributive concessions—shares in the spoils of victory or subsidized costs, for instance—that make coordinated action worthwhile. Lalman and Newman (1990) and Morrow (1991a) have examined the question of alliance formation, for example, when the interests of the parties are not to attain mutual security gains. Morrow (1991a) in particular shows theoretically and empirically that states can coordinate by joining a mutual alliance in which one gains improved security against threats from enemies at the expense of some loss in foreign policy autonomy and the other sacrifices some degree of its own security, by risking entanglement in its partners’ problems, in exchange for improvement in its ability to act independently on foreign policy matters.
Not all coordination solutions need to involve costs, but generally those that impinge as well on distribution questions do when the issue is a one-shot circumstance. Even with distributional differences at play, however, it is sometimes possible to find ways to coordinate as long as the situation involves indefinitely repeating interaction. In these circumstances, cheap talk can help identify a coordination mechanism whereby players alternate on distributional gains or find some other distributional scheme that leaves them all better off in the long run (Taylor, 1976; Axelrod, 1984). Because many foreign policy problems are inherently of unknown duration—such as negotiations over nuclear policy with North Korea or Iran—it is possible (though difficult) to find coordinated solutions to differences in distributional interests.
Patience calibrates the value a given cost or benefit has tomorrow compared to the same cost or benefit today. The more patient a person is, the closer the future value is to the current value. Greater impatience, therefore, means more greatly discounting future costs or benefits compared to the same values today.
Repeated strategic situations have important qualities that separate them from single-shot games. When games are repeated an indefinite or unknown number of times, then there can be a great many equilibria. Even for situations that in single play have only one equilibrium strategy, as is true for the prisoner’s dilemma, with indefinite repetition a vast number of equilibria are possible. One is when players always cooperate with each other. In the single-shot game they cannot rationally do so. The key to cooperation in these circumstances is that with enough time and patience, the cumulative benefits of cooperation can outweigh the short-term incentive to cheat or behave aggressively (Axelrod, 1984).8 Repeated interaction, however, is not always beneficial. Just as reducing uncertainty sometimes exacerbates a situation, so too can repeated interaction. To anticipate whether repetition promotes conflict or cooperation, it is important to understand how patient or impatient players are and what the sequence of gains and losses looks like. For instance, repeated play can lead to cooperation in the prisoner’s dilemma if the participants in the game are patient, that is, if they value continuous modest benefits more than they value larger immediate gains followed by ongoing greatly reduced benefits. The more impatient a player is, the more difficult it is to inspire cooperation because the anticipated cumulative benefits are heavily discounted.
In an arms race, in contrast, patience can make cooperation less likely (Powell, 1999; Slantchev, 2003). Arms races are characterized by absorbing costs now to prevent defeat later. Governments recognize that what they spend on arms comes at the expense of consumption, savings, and other beneficial aspects of a national economy. They also recognize that if they fail to spend while a rival builds up its military might, then they make themselves vulnerable by giving their adversary a first-strike advantage. The more highly valued the future flow of benefits is that can be derived by using a first-strike advantage by conquering a rival, the more willing a regime’s leaders are to bear the high cost of spending more money on arms today to ensure victory and a steady stream of benefits in the future. In this case, costs are borne upfront and a stream of gains results from undertaking
those costs now. Therefore, the more valuable the future, time-discounted cumulative worth of those gains, the more a state is inclined to spend on arms in pursuit of the long-term gains from a first-strike advantage. In this case impatience makes leaders more reluctant to sacrifice today for tomorrow’s gains. Patience has the opposite effect.
Game theory models of patience remind us to be careful not to leap to general conclusions from specific insights. Patience neither leads inevitably to cooperation nor does it lead inevitably to conflict. Which arises depends on the structure of the circumstance. Thus, the intelligence analyst can capitalize on the conditional predictions of models of strategic interaction to provide insight into what might look like unique circumstances in any specific case.
EMPIRICAL CONSIDERATIONS RELATED TO STRATEGIC INTERACTION
Hypotheses derived from game theory models can be difficult to test. This is so because actions are, as we have discussed, part of an equilibrium strategy intended to produce the best outcome each player can get. This means some outcomes are placed off the equilibrium path because of strategic consideration. Some common problems in moving from hypotheses to empirical evaluations result from a failure to attend to these strategic considerations. Here I discuss two of these empirical challenges.
Because potential outcomes are placed off the equilibrium path when there is a strategy that is expected to produce a better result for a player, what we get to observe has been selected based on the anticipated inferior results of what we do not get to observe: the results off the equilibrium path. This means that outcomes—and the cases we can observe—are the product of selection effects, or the elimination of certain possible actions because of their expected negative consequences. Another strategic concern that shapes the cases we can examine is closely associated with selection effects. Many—perhaps most—foreign policy decisions reflect endogenous choices, or choices that create the value attached to explanatory variables—such as the demands made by contending sides in a dispute—to improve each player’s expected results. For example, security-conscious calculations about what to seek as the resolution of a dispute take into account not only what the player wants, but also what the player anticipates will minimize its risks of a particularly bad outcome (Morrow, 1991b; Smith, 1998). In this way, endogenous, strategic decision making can lead to selection effects in that the anticipation of alternative outcomes shapes current choices so that, in a sense, causality is reversed, with the future “causing” current decisions. Let’s examine each of these factors more closely. Then we will be ready to turn to prediction.
Selection Effects: Confounding Inferences
Nearly all historical research on topics such as the causes of big wars, or on nuclear proliferation, both topics of likely concern for intelligence analysts, suffers from selection effects. Scholars concerned with big wars, for instance, almost never examine events that threatened to become big wars but did not escalate beyond low levels of dispute. Scientific analyses, with a strong concern for control groups, and especially game theoretic analyses with their emphasis on counterfactual actions, help reduce errors of inference that may prevail in other forms of investigation. A mind experiment regarding war can help clarify this claim.
All else being equal, consider which events in history were probably expected to yield bigger costs if they became wars: those that actually became wars or those that were resolved peacefully through negotiations. One important reason for finding a negotiated resolution to an international dispute is that the costs of fighting are expected to be too high. When the costs of war are expected to be relatively low, however, then fighting becomes more acceptable.9 It follows that we cannot understand the causes of big wars without examining many crises that had the potential to become big wars, but were averted by reaching a negotiated settlement beforehand. The Cuban Missile Crisis is a nearly perfect example of such an event and has been widely studied (Allison and Zelikow, 1999). But one can see similar patterns in a mostly forgotten dispute between Bavaria and Prussia over Hesse in 1850. In that case, there is little historical research perhaps because, in the end, almost nothing happened. Yet contemporaneous newspaper accounts of the 1850 dispute were dominated by fears that the conflict would erupt into a general war in Europe. Fear of just such a war prompted Prussia to grant concessions that otherwise might not have been granted to a rival as weak as Bavaria, or even to Bavaria’s Austrian allies (Bueno de Mesquita and Lalman, 1992).
We see these effects even more dramatically in cases in which nothing at all happened, so we do not even get to observe a low-level conflict. Selection effects that result in “the dog that didn’t bark” often lead to selection bias in empirical research. Let me illustrate how strategic selection effects and the case selection bias they lead to can result in unwarranted inferences by discussing the reputed unreliability of military alliances.
Here is a useful fact with which to begin: Often—perhaps as often as 70 percent of the time, depending on how the estimate is done—when a nation with allies is attacked, the allies, despite their treaty obligations, fail
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 partner “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 unreliable, 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 unreliable if an attack has taken place. A, after all, has already taken into account
the anticipated reliability of C’s commitment as part of A’s strategic decision 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 expectation, 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 supports the selection argument regarding alliance reliability (Smith, 1996b).
Dominant arguments among international relations scholars and practitioners 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).
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 independent 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 variables do not depend on expectations about how they will shape outcomes is problematic. When choices are made strategically, they are forward looking. 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 Christmas tree sales cause Christmas or the anticipation of Christmas causes tree sales. Behind this example lies an important consideration for policy
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; Wallace, 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 preceded by arms races. The arms build-up is taken as exogenous, as independent 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 explanatory 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
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 challenging 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 statistical 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 models, 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 endogenous 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 security matters. Indeed, Stanley Feder (2002), a former Central Intelligence Agency (CIA) analyst and national intelligence officer, emphasizes the virtues 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
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 models 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. Fortunately, 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.
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 transparency; 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 socialscience–oriented methods.
Game theory forecasting methodology used to evaluate political decisions, 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.
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 information, 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 requirement 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 players have bounded, that is, limited rationality, are two modifications to standard 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
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 theoretic 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.
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
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.
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 mediation 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 University Press.
Bueno de Mesquita, B., and W. H. Riker. 1982. Assessing the merits of selective nuclear proliferation. 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.
Bueno de Mesquita, E., and E. Dickson. 2007. The propaganda of the deed: Terrorism, counterterrorism, and mobilization. American Journal of Political Science 51(2):364–381.
Bueno de Mesquita, B., A. Smith, R. M. Siverson, and J. D. Morrow. 2003. The logic of political survival. Cambridge, MA: MIT Press.
Byron, M., ed. 2004. Satisficing and maximizing: Moral theorists on practical reason. New York: Cambridge University Press.
Calvert, R. L. 2006. Deliberation as coordination through cheap-talk. Presented at Midwest Political Science Association annual meeting, April 20–23, Chicago, IL. Available: http://www.nyu.edu/gsas/dept/politics/seminars/Calvert_Paper.pdf [accessed October 2010].
Coletta, D., and E. Gartzke. 2003. Testing war in the error term. International Organization 57(Spring):445–448.
Crawford, V., and J. Sobel. 1982. Strategic information transmission. Econometrica 50:1431–1451.
Diehl, P. F., and M. J. C. Crescenzi. 1998. Reconfiguring the arms race war debate. Journal of Peace Research 35(1):111–118.
Downs, G. W., D. M. Rocke, and P. N. Barsoom. 1996. Is the good news about compliance good news about cooperation? International Organization 50:379–407.
Drezner, D. W. 1999. The sanctions paradox. New York: Cambridge University Press.
Egorov, G., and K. Sonin. 2005. The killing game: Reputation and knowledge in politics of succession. Game Theory and Information. Available: http://ideas.repec.org/p/wpa/wuwpga/0505003.html [accessed May 2010].
Fearon, J. D. 1991. Counterfactuals and hypothesis testing in political science. World Politics 43(January):169–195.
Fearon, J. D. 1994. Domestic political audiences and the escalation of international disputes. American Political Science Review 88:577–592.
Fearon, J. D. 1995. Rationalist explanations for war. International Organization 49:379–414.
Feder, S. 1995. Factions and policon: New ways to analyze politics. In H. Westerfield, ed., Inside CIA’s private world: Declassified articles from the agency’s internal journal, 1955–1992 (pp. 274–293). New Haven, CT: Yale University Press.
Feder, S. A. 2002. Forecasting for policy making in the post-cold war period. Annual Review of Political Science 3:149–166.
Fey, M., and K. Ramsay. 2007. Mutual optimism and war. American Journal of Political Science 51(4):738–754.
Gaddis, J. 1992. International relations theory and the end of the cold war. International Security 17(3):323–345.
Gartzke, E. 1999. War is in the error term. International Organization 53:567–587.
Gibler, D. M., T. J. Rider, and M. L. Hutchison. 2005. Taking arms against a sea of troubles: Conventional arms races during periods of rivalry. Journal of Peace Research 42(2):131–147.
Goemans, H. E. 2008. Which way out: The manner and consequences of losing office. Journal of Conflict Resolution 52(6):771–794.
Harsanyi, J. C. 1967–1968. Games with incomplete information played by “Bayesian” players. Management Science 14:157–182, 320–324, 486–502.
Hufbauer, G. C., J. J. Schott, K. A. Elliott, and B. Oegg. 2007. Economic sanctions reconsidered, 3rd ed. Washington, DC: Peterson Institute for International Economics.
Huth, P. K. 1988. Extended deterrence and the prevention of war. New Haven, CT: Yale University Press.
Huth, P. K. 1996. Standing your ground: Territorial disputes and international conflict. Ann Arbor: University of Michigan Press.
Huth, P. K., and B. M. Russett. 1984. What makes deterrence work? Cases from 1900 to 1980. World Politics 36:496–526.
Jones, B. F., and B. A. Olken. 2009. Hit or miss? The effect of assassinations on institutions and war. American Economic Journal: Macroeconomics 1(2):55–87.
Kahneman, D., and A. Tversky. 1984. Choices, values and frames. American Psychologist 39(4):341–350.
Kahneman, D. and D. T. Miller. 1986. Norm theory: Comparing reality to its alternatives. Psychological Review 93:136–153.
Karl, T. 1990. Dilemmas of democratization in Latin America. Comparative Politics 23:1–23.
Kim, W., and J. D. Morrow. 1992. When do power shifts lead to war? American Journal of Political Science 36:896–922.
King, G., and L. Zeng. 2001. Improving forecasts of state failure. World Politics 53(4):623–658. Kydd, A. 2005. Trust and mistrust in international relations. Princeton, NJ: Princeton University Press.
Kydd, A., and B. F. Walter. 2002. Sabotaging the peace: The politics of extremist violence. International Organization 56(2):263–296.
Lalman, D., and D. Newman. 1990. Alliance formation and national security. International Interactions 16:239–254.
Lapan, H. E., and T. Sandler. 1988. To bargain or not to bargain: That is the question. American Economic Review 78(2):16–21.
Lapan, H. E., and T. Sandler. 1993. Terrorism and signaling. European Journal of Political Economy 9(3):383–397.
Leeds, B. A. 2003. Alliance reliability in times of war: Explaining decisions to violate treaties. International Organization 57(Fall):801–827.
Leeds, B. A., A. G. Long, and S. McLaughlin Mitchell. 2000. Re-evaluating alliance reliability: Specific threats, specific promises. Journal of Conflict Resolution 44:686–699.
Leeds, B. A., J. Ritter, S. McLaughlin Mitchell, and A. G. Long. 2002. Alliance treaty obligations and provisions, 1815–1944. International Interactions 28:261–284.
Martin, L. L. 1993. Coercive cooperation. Princeton, NJ: Princeton University Press.
McDermott, R. 1998. Risk-taking in international politics. Ann Arbor: University of Michigan Press.
McDermott, R. 2007. Presidential leadership, illness and decision making. New York: Cambridge University Press.
Morrow, J. D. 1987. On the theoretical basis of a measure of national risk attitudes. International Studies Quarterly 31:423–443.
Morrow, J. D. 1991a. Alliances and asymmetry: An alternative to the capability aggregation model of alliances. American Journal of Political Science 35:904–933.
Morrow, J. D. 1991b. Electoral and congressional incentives and arms control. Journal of Conflict Resolution 35:243–263.
Morrow, J. D. 1994. Modeling the forms of cooperation: Distribution versus information. International Organization 48:387–423.
Niou, E., P. Orde shook, and G. Rose. 1989. The balance of power. Cambridge, UK: Cambridge University Press.
North, D., J. J. Wallis, and B. Weingast. 2009. Violence and social orders: A conceptual framework for interpreting recorded human history. New York: Cambridge University Press.
O’Donnell, G., P. Schmitter, and L. Whitehead, eds. 1986. Transitions from authoritarian rule. Baltimore, MD: Johns Hopkins University Press.
O’Neill, B. 2001. Risk aversion in international relations theory. International Studies Quarterly 45:616–640.
Powell, R. 1990. Nuclear deterrence theory. Cambridge UK: Cambridge University Press.
Powell, R. 1999. In the shadow of power. Princeton, NJ: Princeton University Press.
Ray, J. L., and B. M. Russett. 1996. The future as arbiter of theoretical controversies: Predictions, explanations and the end of the cold war. British Journal of Political Science 26(4):441–470.
Richardson, L. F. 1960. Arms and insecurity. Chicago, IL: Quadrangle.
Riker, W. H. 1996. The strategy of rhetoric. New Haven, CT: Yale University Press.
Rosendorff, P., and T. Sandler. 2004. Too much of a good thing? The proactive response dilemma. Journal of Conflict Resolution 48(4):657–671.
Sabrosky, A. 1980. Interstate alliances: Their reliability and the expansion of war. In J. D. Singer, eds. The correlates of War II: Testing some realpolitik models. New York: Free Press.
Sargent, T. 1994. Bounded rationality in macroeconomics. New York: Oxford University Press.
Sartori, A. 2005. Deterrence by diplomacy. Princeton, NJ: Princeton University Press.
Schneider, G., D. Finke, and S. Bailer. 2010. Bargaining power in the European Union: An evaluation of competing game–theoretic model. Political Studies 58(1):85–103.
Schultz, K. 1998. Domestic opposition and signaling in international crises. American Political Science Review 92:829–844.
Shepsle, K. A. 1979. Institutional arrangements and equilibrium in multidimensional voting models. American Journal of Political Science 23:27–59.
Simon, H. A. 1957. Models of man: Social and rational. New York: John Wiley and Sons.
Siverson, R. M., and J. King. 1980. Attributes of national alliance membership and war participation, 1816–1965. American Journal of Political Science 24(1):1–15.
Slantchev, B. 2003. The power to hurt: Costly conflict with completely informed states. American Political Science Review 97(1):123–133.
Smith, A. 1996a. The success and use of sanctions. International Interactions 21(3):229–245.
Smith, A. 1996b. To intervene or not to intervene: A biased decision. Journal of Conflict Resolution 40(1):16–40.
Smith, A. 1998. International crises and domestic politics. American Political Science Review 92(3):623–638.
Smith, A. 1999. Testing theories of strategic choice: The example of crisis escalation. American Journal of Political Science 93(4):1,254–1,283.
Sonin, K., and G. Egorov. 2005. Dictators and their viziers: Agency problems in dictatorships. Available: http://www.nyu.edu/gsas/dept/politics/seminars/sonin_s05.pdf [accessed October 2010].
Spence, M. 1973. Job market signaling. Quarterly Journal of Economics 86:355–374.
Taylor, M. 1976. Anarchy and cooperation. London, UK: John Wiley and Sons.
Tetlock, P. 2005. Expert political judgment. Princeton, NJ: Princeton University Press.
Tetlock, P., and A. Belkin. 1996. Counterfactual thought experiments in world politics. Princeton, NJ: Princeton University Press.
Thomson, R., F. N. Stokman, C. H. Achen, and T. König., eds. 2006. The European Union decides. Cambridge UK: Cambridge University Press.
Vasquez, J. A. 1997. The realist paradigm and degenerative versus progressive research programs: An appraisal of neotraditional research on Waltz’s Balancing Proposition. American Political Science Review 91(4):899–912.
Vasquez, J. A. 2009. Territory, war, and peace. New York: Routledge.
Wallace, M. 1982. Armaments and escalation: Two competing hypotheses. International Studies Quarterly 26:37–56.
Ward, M. D., R. M. Siverson, and X. Cao. 2007. Disputes, democracies, and dependencies: A re-examination of the Kantian peace. American Journal of Political Science 51(3):583.
Wittman, D. 1979. How a war ends: A rational model approach. Journal of Conflict Resolution 23(4):743–763.
Wittman, D. 2009. Bargaining in the shadow of war: When is a peaceful resolution most likely? American Journal of Political Science 53:588–602.
Wu, S. 1990. To attack or not to attack: A theory and empirical assessment of extended immediate deterrence. Journal of Conflict Resolution 34:531–552.