A long-standing principle of international relations theory is that coercive threats are more effective, on average, when they come from powerful states. Indeed, it seems intuitive that strong powers would make more potent threats since they can threaten especially severe punishment for noncompliance.Footnote 1 But the historical record shows that the failure of asymmetric compellent threats has been a persistent feature of international crises across both geography and time.Footnote 2 As far back as the Peloponnesian War, for example, Thucydides told of imperial Athens's failure to intimidate the tiny island of Melos into joining its circle of allies. In the mid-nineteenth century, Turkey's rejection of a Russian ultimatum led to the Crimean War; a decade later, the Seven Weeks' War erupted in part because Prussia's mighty army could not coerce weaker neighbors such as Saxony, Hanover, and Electoral Hesse into joining Bismarck's confederation without a fight. Explicit threats likewise failed to secure safe passage for the German army through Belgium and Luxembourg at the outset of World War I. Italy failed on multiple occasions during the 1930s to compel an isolated Albania to do its bidding; during the same period, imperial Japan met resistance to its threats from a weak and internally riven China. In 1982, Argentina's military junta refused to roll back its occupation of the Falkland Islands in the face of an explicit British ultimatum. And throughout the 1980s, South African threats failed to compel Botswana, Zambia, and Zimbabwe to crack down on guerilla incursions launched from their territory. In all of these cases, the balance of military power was stacked heavily in favor of the aggressors, yet their threats were unsuccessful.
Asymmetric compellence failures likewise resonate strongly in U.S. foreign policy. Since the end of World War II, the United States has targeted mostly weaker adversaries with its threats, but usually those threats have not worked.Footnote 3 In the past two decades, for example, Panama, Iraq, Serbia, and Afghanistan all defied U.S. threats despite being comparatively weak. Indeed, the costly occupation of Iraq, now drawing to a close after nearly eight years, was preceded by a failed ultimatum against Saddam Hussein. Why has U.S. primacy apparently not translated into greater coercive leverage against small adversaries?
These compellence failures are puzzling because they seem to violate the traditional notion that threats are more likely to work when the state issuing them holds a large military advantage. Are these examples simply rare exceptions to the rule, or do they suggest a broader pattern? In this article, I argue that they are probably not the anomalies they appear to be. Building on a standard model of interstate crisis bargaining, I argue that an abundance of military power can be self-defeating in coercive diplomacy. The analysis shows that a challenger's strength can interfere with its ability to evaluate an opponent's resolve and propose a mutually acceptable revision of the status quo. In short, a challenger's military power exacerbates information problems that make its threats less likely to succeed.
The analysis rests in large part on a logic of reputation-building. When a target capitulates to a compellent threat, it reveals information about the limits of its resolve. In other words, complying with a threat entails reputation costs for the target—costs that are particularly high if the target believes that the challenger will exploit its newfound knowledge to make additional demands in the future. Even if the demand itself seems reasonable, the risk that it might presage further demands might nevertheless motivate the target to fight unless the challenger can make the risk worthwhile by demanding less or offering compensation. A successful compellent threat requires the challenger and target to agree on a fair “price” for the target's reputation: if the challenger underestimates the target's reputation costs, it will offer too little compensation and the threat will fail.
A challenger's military power increases the risk of such miscalculations by making it more difficult for adversaries to settle on a common estimate of the target's reputation costs. The reason is that as a challenger's ability to project military power grows, the value of the target's reputation depends increasingly on whether it believes that the challenger will make additional threats. But since the challenger's intentions are known only to itself, the two sides may reach very different conclusions about this likelihood. Realizing that the target has incentives to exaggerate its fears of the future to get a better deal today, the challenger may insufficiently compensate the target's perceived reputation costs, causing the threat to fail. In contrast, when a challenger lacks the material ability to project power—whether due to physical weakness or geographic distance—its private preferences are less relevant. Both sides can easily agree about the improbability of future threats, even if they disagree about whether the challenger secretly covets more of the target's possessions. This fact facilitates mutual agreement about the target's (low) reputation costs and increases the chances of a properly calibrated demand in the status quo. In this way, power can impede challengers' efforts to buy off the reputational interests of their targets, making compellent threats less likely to work. Even when a challenger's threats are completely credible, the balance of capabilities is publicly known, and settlements are enforceable, fears about a challenger's future intentions can motivate rational targets to fight losing wars to deter further aggression.
The argument I present in this article contains two important implications for the study of reputations in international crisis bargaining. First, this article offers a more complete rationalist theory of reputations in military crises by specifying why challengers may be unable to buy off reputation-minded opponents. Although it is often suggested that states might stand firm in crises to deter future challenges, this is an insufficient explanation for why threats against such states might fail. The reason is that if one participant in a dispute has incentives to induce an inefficient outcome (that is, war) in order to look tough, then the other participant should have equally strong incentives to prevent that outcome by making smaller demands or by offering larger side payments. In other words, reputations are not only worth building; they are also worth accommodating. A complete reputational explanation for coercive failures therefore must explain why the target's reputational interests could not be accommodated by the challenger.
Recent scholarship about reputation-building in international politics illustrates this problem. For instance, Walter argues that a government might fight a civil war against a secessionist group in order to look tough and discourage other rebel groups from making their own demands.Footnote 4 But this explanation raises a puzzle: why did the secessionist group not anticipate this dynamic? If the secessionist group had known about the government's reputation problem (which it had incentives to do), it might have offered some additional side payment to offset the government's reputation costs, thereby avoiding a costly war. Reputation-building incentives alone cannot explain bargaining failures—one must also explain why a challenger cannot simply recognize its adversary's reputation problem ahead of time and propose a more attractive deal to ameliorate it.Footnote 5 But scholarly treatments of reputation-building in international crises tend to overlook this problem, often assuming it away altogether with models that do not allow challengers to make such accommodations.Footnote 6
The common “balance of interests” explanation for compellence failure suffers from a similar problem. This explanation asserts that threats fail when the stakes in asymmetric disputes are more important to the weaker side.Footnote 7 However, most bargaining models of war imply that challengers have strong incentives to anticipate (and accommodate) such imbalances of interests in order to avoid the inefficiencies of war.Footnote 8 A complete explanation for compellence failure therefore must specify why a challenger cannot recognize an unfavorable balance of interests beforehand and attenuate its demands accordingly. The model evaluated in this study addresses this problem by allowing challengers to strategically adjust their demands in response to reputational dynamics. The model helps explain why powerful, rational challengers may be more likely to make mistakes when devising their compellent threats, despite having incentives to avoid them.
Second, this article questions recent findings that reputations do not matter in crisis bargaining. The central question driving much research about reputation in interstate crises asks whether a state can become known for being the type that generally upholds its commitments—in other words, whether a state can obtain a reputation for honesty in international diplomacy.Footnote 9 Scholars such as Press argue that the answer is no: leaders predict an adversary's behavior by considering its power and interests, he argues, not by weighing broad judgments about its character. Since power and interests inevitably vary from crisis to crisis, this view asserts, a state's past actions have no bearing on crisis outcomes in the status quo.Footnote 10
The discussion below suggests that this conclusion is overstated. Although military crises are often about different issues, they all share one crucial similarity: military conflict is always a possible outcome. It is reasonable, then, to expect that beliefs about others' sensitivity to the costs of war might carry over from crisis to crisis, irrespective of the nature of the dispute. In other words, fighting may be useful for communicating cost-tolerance, even if it does not communicate a general penchant for credibility or honesty. In this way, all military crises may be at least partially interdependent, even when the issues triggering them are not the same. Empirical research showing that one particular type of reputation—that is, a reputation for keeping (or breaking) verbal commitments—appears not to matter in military crises therefore should not lead us to infer that reputations in general are irrelevant in international disputes.
The remainder of this article proceeds as follows. First, I locate three potential explanations for asymmetric compellence failure in the literature on international conflict and find them poorly suited to this puzzle. Second, I describe a strategic model of crisis bargaining and explain why it is useful for investigating the effectiveness of compellent threats. Third, I characterize the model's equilibria and explore its basic logic. The fourth section evaluates the causes of compellence failure in the model and explains why it is more likely when challengers are powerful. The final section illustrates the model's mechanisms with the example of the 1939 Russo-Finnish crisis, in which Soviet compellent threats failed to persuade Finland to make fairly minimal territorial concessions. The article concludes with several implications for the study of coercion in international relations.
Possible Explanations
Why do compellent threats from extremely powerful states often fail? Ready answers can be found in the theoretical literature on the causes of war. Here I consider three plausible accounts and argue that while they surely help to explain many international crises, they are not very useful for understanding the narrower class of compellence failures in which the challenger has a lopsided military advantage.
First, false optimism might explain the failure of asymmetric compellent threats: if a crisis participant cannot effectively communicate its military strength, its adversary might reject a peaceful resolution in the mistaken belief that its power entitled it to a better deal.Footnote 11 In crises where the challenger is overwhelmingly powerful, however, this explanation is unconvincing, since miscalculations about relative power are probably least likely when the balance of power is heavily tilted toward one side. Uncertainty about relative capabilities is commonplace among military peers, whose strength vis-à-vis each other depends on training, tactics, and other factors that one or both sides cannot observe. But as Wagner has argued, intangible factors become less decisive when the observable balance of forces is lopsided, increasing the likelihood that the two sides will agree about the probable outcome of a fight.Footnote 12 In 1914, for example, the enormous material disparity between the German and Belgian armies helped military planners on both sides reach virtually identical judgments about the balance of power. Belgium's decision to refuse Germany's demands was taken not in a fit of exuberance, but rather with the reluctant acknowledgment that defeat would be inevitable despite the nation's external security guarantees.Footnote 13
Second, a compellent threat from a powerful challenger might be rejected if the target believes it to be a bluff. This explanation, however, has trouble accounting for compellence failures that lead to war. The reason is that a challenger's initial use of force would dissipate any uncertainty about whether or not its threat was honest. The target may initially disbelieve the threat, but the outbreak of military hostilities would immediately correct this miscalculation. For war to follow, the target must decide to fight anyway.Footnote 14 When Otto von Bismarck ordered the invasion of tiny Electoral Hesse following a failed ultimatum in 1866, for example, Hessian leaders learned of the impending assault three days before Prussian troops reached their territory.Footnote 15 If the Hessians thought that Bismarck was bluffing, they could have backed down once they realized their error—in other words, as soon as Prussian troops began to march.Footnote 16 But since Bismarck's threat failed even after his resolve was revealed, Hessian miscalculation seems an unlikely explanation.
Third, a compellent threat could fail if the target feared that acquiescing would strengthen the challenger militarily and change the balance of power. In other words, target states might refuse compellent threats simply to prevent challengers from growing stronger, since the challenger might want to renegotiate once its position improved.Footnote 17 But this explanation seems implausible under conditions of wide asymmetry. When the challenger already boasts a preponderance of power, acceptance of its demands is unlikely to alter the balance of power in any perceptible way. Even when strategically important objects are at stake, there is little that a challenger could demand that would have much impact on an already-skewed balance of bargaining leverage.Footnote 18 It seems farfetched to suggest, for instance, that the transfer of the Sudetenland—a paradigmatic example of strategic territory—had more than a marginal effect on the net balance of power between Germany and Czechoslovakia in 1938.
A Model of Compellent Threats
In this section I describe a model of compellence and crisis bargaining that offers a different set of answers to the puzzle of compellence failure. In its most basic form, first described in an international relations context by Fearon,Footnote 19 the model contains two strategic players: a challenger (state A) and a target (state B). The target stands in possession of some disputed object, the value of which is normalized (without loss of generality) to 1. The challenger then issues a compellent threat in which it demands some share (x 1) of the item and threatens military punishment if the target does not comply.Footnote 20 The target may accept or reject the demand: if it accepts, redistribution takes place accordingly, but if it refuses, the two states fight a winner-take-all war over it, each paying some non-negative cost (c i) for fighting the war.Footnote 21 Assume that the balance of capabilities is sufficiently clear so that both sides acknowledge the challenger's chances of winning a war to be p. The challenger's expected value for fighting a war (that is, a failed threat) is therefore p − c A, whereas the target expects to receive 1 − p − c B by fighting.
Next, I stipulate that the initial round of bargaining takes place in the shadow of a possible future crisis. Once the states observe the outcome of the first dispute, there is a possibility (φ) that a second dispute will arise over an object whose value is π ∈ (0,∞).Footnote 22 The same bargaining procedure takes place, with the challenger demanding a share of the new object (x 2) and the power and cost parameters p and c i remaining the same. Once the second dispute is resolved, the game ends. The complete model is illustrated graphically in Figure 1.
The compellence game
Information and Beliefs
Both players in the model are informed about p, which can be roughly characterized as the balance of military capabilities.Footnote 23 What is crucial, however, is not that these beliefs are correct, but rather that the two sides simply agree on them.Footnote 24 Stipulating agreement about p eliminates the possibility that private information about military capabilities will change the dynamics of the bargaining. The only piece of information not known to both players is the target's value for the cost of fighting—that is, the intrinsic value it places on the human, material, and political damage that it would suffer during war—relative to the stakes of the crisis (c B). The target knows its own value, but the challenger is aware only that c B falls within some range of possible values. Assume that before the game begins c B is drawn from a uniform distribution across the interval [0,C], where C represents the maximum possible value that c B might take.Footnote 25 One might thus conceive of C as the target's “reputation for resolve” at the outset of the game—when the challenger believes that the target's cost of war is probably low, then C is small. Conversely, when the challenger believes that the target might have high costs, then C is larger. The challenger must therefore select its optimal demands in each round within the framework of its uncertainty about the target's resolve.
Four simplifying assumptions of the model deserve explicit clarification here. First, the model adopts an ultimatum protocol, disallowing counteroffers and permitting the target only two choices: acquiesce (Acq) or fight (F). Second, once the challenger issues a threat, it is not permitted to back down. As a consequence, its threat is completely credible—the target knows that bluffing is impossible, so it is effectively prohibited from refusing a demand in hopes that the challenger will fail to carry out its threat. Third, the balance of military capabilities (p) is assumed to remain constant from one crisis to the next, irrespective of the outcome of the first dispute. The model thus implicitly assumes that neither war nor settlement conveys upon either state any military advantage that it did not enjoy before.Footnote 26 Finally, I stipulate that the players have accurate and complete information about the balance of military power between them at all times.
These assumptions are widely used in models of international crisis bargaining, but one might reasonably object to them on empirical grounds.Footnote 27 In international crises, after all, back-and-forth bargaining is common, and threats are never perfectly credible; moreover, wars and crisis settlements often alter the balance of power, and knowledge about other states' military capabilities is inevitably incomplete. Yet this cost in real-world fidelity yields an important analytical benefit: the assumptions effectively “stack the deck” against compellence failure. The failed threats noted at the outset of this article are puzzling in part because so many factors would seem to have favored their chances for success; it is useful, then, to build a model simulating highly favorable conditions for the challenger to identify dynamics that might help illuminate these cases. The model's take-it-or-leave-it protocol, for instance, favors compellence success by precluding targets from using counteroffers to buy time or to whittle away at the challenger's demands. The second assumption restricts the challenger from backing down once a threat is issued, so its threat to fight is perfectly credible—the target knows with certainty that war will result if it refuses the challenger's demand. Third, because the outcome of the crisis is assumed to have no effect on the balance of power, the target need not fear that capitulation will cause the challenger to grow stronger. Finally, by stipulating that both sides in the model are accurately informed about the balance of power, the fourth assumption eliminates the possibility that a disagreement about relative capabilities could lead to an unsuccessful threat. Each assumption undoubtedly violates one's empirical sensibilities, but investigating how compellent threats might fail despite seemingly favorable conditions can help generate leverage for explaining the most puzzling empirical cases.Footnote 28
Equilibria
It is straightforward to show that if the target's level of resolve were public knowledge, there would be only one subgame perfect outcome of the model: successful compellence. The clairvoyant challenger would demand x 1 = p + c B in the first round, and x 2 = πp + c B (or, if this demand exceeds the value of the “pie,” simply π) in the second round. Being exactly equal to the target's value for fighting, the target would accept both demands, and fighting would be avoided. In other words, appeasement would occur even though the challenger cannot commit to future restraint, since the target knows it cannot change the challenger's beliefs about c B.
Compellence always succeeds with complete information because the challenger knows exactly how to calibrate its threat to induce the target to give in. But in the incomplete-information version of the model, compellent threats fail precisely because challengers do not know their adversaries' level of resolve (c B). The introduction of uncertainty creates the possibility that the challenger will guess wrong and make a threat that proves unacceptable to the target.
There are two types of pure-strategy equilibria in the incomplete-information model: a separating equilibrium in which the challenger intentionally designs its threat so that it carries a risk of failure, and a pooling equilibrium in which the costs of war persuade the challenger to make only a bare minimum set of demands. In the separating equilibrium, only targets with high costs for fighting acquiesce to the threat, while those with low costs always refuse. In the pooling equilibrium, the challenger's demands are so minimal that all targets opt for appeasement, no matter how small their costs for fighting. In the next section I characterize the strategies that comprise these solutions; a proof is in the appendix.
Challenger's Strategy in the Separating Equilibrium
In the separating equilibrium, A issues the following first-round demand, which I call x 1★ : p + [(C − c A)/2] − φ[(C + c A)/4]. If B acquiesces in the first round, then in the second crisis A will make a “high” demand, which I call x2★, equal to πp + [(C − c A)/2]. But if B fights in the first round, then A must adjust its second-round demand downward. I call this “low” demand x2★, and it is equal to πp + [(C − 3c A)/4].
The intuition here is that the challenger finds itself facing a target whose resolve is unknown and decides to take a risk that will enable it to learn new information about where c B lies along the interval from 0 to C . With the possibility of a second crisis looming, the challenger issues a first-round threat that will separate targets into two general types based on their level of resolve. The most highly resolved targets will stand firm, while all others will capitulate. Specifically, if the target acquiesces to the first threat, then the challenger will know that c B equals or exceeds a critical threshold: c B ≥ (C − c A)/2; conversely, if the target chooses to fight, then it must be the case that c B < (C − c A)/2. Upon observing either of these outcomes, the challenger can then use its new information to adjust its second-round threat accordingly.
For the challenger to learn anything useful about the target's resolve, then, its initial threat must be severe enough to incur some possibility of failure. A low-level demand (specifically, the pooling demand x 1 = p) would not help an observer discern between resolute and irresolute targets, since both types will acquiesce. Instead, to be informative, compellent threats must be ambitious enough so that they induce only highly resolved states to resist. The catch is that such demands also carry a greater risk of failure—indeed, that risk is what makes them informative. The risk of compellence failure therefore can be characterized as the price challengers pay to learn useful information about their targets' resolve.
The separating equilibrium is supportable only when the challenger's costs for fighting are sufficiently low—specifically, if c A ≤ C. In other words, as long as it is possible that the target's costs might equal (or exceed) those of the challenger, then it will be profitable to learn more about the target's resolve. But if there is no possibility that the challenger has lower costs (that is, if c A > C), then playing this strategy turns out not to be worthwhile.
Challenger's Strategy in the Pooling Equilibrium
In the event that the challenger is certain that its costs for fighting exceed those of the target (c A > C), then playing a separating strategy is no longer optimal. Instead, the challenger will demand p in the first round and πp in the second round. Since even the most resolved target—that is, a target with no cost for fighting (c B = 0)—will acquiesce to these demands, the target's response in the first round conveys no new information about its resolve.
Target's Strategy
The target's first-round equilibrium behavior can be described by distinguishing among three types of targets according to their position along the continuum of possible values of c B. These types, which one might label “weak,” “moderate,” and “tough,” adopt the following decision rules for responding to the challenger's first-round threat:
1. “Weak” target: if the target's costs for fighting equal or exceed (C − c A)/2, then only demands greater than p + c B − φ[(C + c A)/4] will motivate it to fight in the first round.
2. “Moderate” target: if the target's costs for fighting lie between (C − 3c A)/4 (inclusive) and (C − c A)/2, then it will fight if the challenger demands more than p + c B − φ{c B − [(C − 3c A)/4]} and acquiesce otherwise.
3. “Tough” target: if the target's costs for fighting are less than (C − 3c A)/4, then it will refuse first-round threats greater than p + c B and acquiesce otherwise.Footnote 29
Characterizing the target's second round strategy is simpler: regardless of the target's costs, it will fight in the second round if the challenger demands more than πp + c B and acquiesce otherwise. These equilibrium strategies hold irrespective of whether the challenger plays a separating or a pooling strategy.
The Logic of Reputation-Building
The central mechanism driving the target's strategy in the first round of the game is reputation-building. By fighting in the first round even though the challenger's demand might be acceptable on its own terms, weak and moderate targets can get better deals in the second round. As the likelihood of a future crisis increases, the payoff from making this investment increases in tandem. This is shown by comparing the first-round strategies of weak and moderate targets in a one-round game (that is, when φ = 0) and a game in which the possibility of a future crisis exists (φ > 0). Figure 2 illustrates the comparison. When there is no possibility of a second dispute, appeasement is preferable under a considerably wider set of circumstances than when a second dispute is possible. Indeed, when the shadow of the future looms, weak and moderate targets will reject deals (represented by the shaded region) that would have been acceptable in a single-shot interaction.Footnote 30
The target's equilibrium first-round strategy
Uncertainty sits at the core of this logic. By necessity, any strategic engagement involving reputation effects must entail asymmetric information.Footnote 31 The maximum demand acceptable to a target is known to only itself: challengers can at best venture a reasonable guess about an appropriate threat given the military balance. Targets can exploit this fact by withholding information that might indicate their resolve is weak—in other words, by resisting threats that they would really prefer to accept. When a challenger observes a target resisting, it rationally updates its beliefs about the target's likely behavior in later crises. But a reputation can only be built if a state's resolve is inherently unknown to begin with.
The challenger's first-round strategy in the separating equilibrium is designed to accommodate its adversary's incentives to masquerade. Notice that the challenger's optimal demand in the first round, {p + [(C − c A)/2] − φ[(C + c A)/4]}, declines as the likelihood of a future crisis (φ) increases. The intuition is that the challenger must pay a subsidy—expressed in the form of smaller demands or side payments—to offset the target's interest in defending its reputation. As the likelihood of a future dispute increases, the target's value for its reputation grows as well, thus necessitating a larger “discount” on the challenger's demand. In a game where φ = 0—that is, when there is no chance of a future dispute—the challenger's best strategy would be to demand p + [(C − c A)/2]. As the shadow of the future grows and φ increases, however, then the challenger's optimal demand declines.
The Causes of Compellence Failure
I now turn to the central question of this article: when a challenger is extremely powerful, under what conditions might its compellent threats still fail? Recall that, by construction, neither private information about military capabilities nor incredible threats by the challenger are possible scenarios for compellence failure in the model. Relative power also remains constant throughout, so preventive war motives cannot explain unsuccessful threats. Again, it is important to acknowledge that these and other mechanisms (for example, honor or domestic politics) surely have played important roles in causing compellence failures throughout history. As discussed above, however, many of these explanations are a poor fit in instances of asymmetry. Moreover, excluding them from the model stacks the deck in favor of compellence success, thereby consciously restricting the analytical scope to the most puzzling cases.
The question of threat effectiveness can be answered by evaluating the conditions under which fighting occurs in the model (Figure 3). Note that fighting can only occur in the separating equilibrium, since in the pooling equilibrium the challenger is dissuaded from making any threats that carry a chance of failure. Moreover, in the separating equilibrium, fighting is possible in the second round only if there was also fighting in the first round. This is a consequence of the challenger's strategic choice of demands: the proof in the appendix shows that if the target acquiesces in the first round, it is optimal for the challenger to make the highest second-round demand that it is certain will be accepted. In equilibrium, then, acquiescence is never followed by war. The overall likelihood of fighting is thus given simply by the probability of first-round fighting. This probability is equivalent to the likelihood that the target's cost for war c B falls below the challenger's optimal cutpoint and is given by (1/2) − (c A /2C).
Outcomes in the separating equilibrium as the target's costs of fighting vary
An immediate and somewhat counterintuitive implication of this result is that the probability of compellence success (that is, appeasement) increases as the target's reputation improves. If the target has a reputation for cost-tolerance—in other words, if C is low—then the challenger is more likely to choose the pooling demand, which is certain to succeed. As C increases, however, there are greater potential benefits of drawing out irresolute targets by using a separating strategy. Challengers therefore become more likely to issue threats that carry a risk of failure since they might glean valuable information from them. In other words, we are more likely to observe successful threats against targets that are already believed to be highly resolved. This conclusion is pertinent to empirical research about reputations in crises, in which past capitulations often serve as proxy indicators of a poor reputation.Footnote 32 The logic of strategic self-selection implies that, without knowing the nature of the challenger's compellent demands, observed instances of appeasement reveal little about a target state's reputation for resolve.
Divergent Beliefs about the Future
In the separating equilibrium, moderate and tough types always resist the challenger's first-round threat (see Figure 3), whereas weak types always appease. But under certain conditions, weak types might also fight. In particular, if the challenger underestimates the target's expectations about the likelihood of a future dispute (φ), its first-round equilibrium demand will be miscalibrated and some weak types will refuse. In the model, divergent views about the future can be represented by using φi to denote each state's belief about the probability that a second round will be played over a new issue.Footnote 33 Stipulate that the two sides arrive at these beliefs independently and that the target is more convinced that future crises will erupt (thus φB > φA), but the players cannot observe each other's φ value.
What are the consequences of this disparity? If the challenger's costs are low enough to justify a separating strategy, its beliefs about the future (φA) help determine its first-round equilibrium demand, x 1★ = p + [(C − c A)/2] − φA [(C + c A)/4]. But as its estimate of the shadow of the future drops, so does the discount it applies to induce weak targets to capitulate. (Its second-round demand, however, remains independent of φA.) In other words, when the challenger does not anticipate making demands in a future dispute, it will make higher demands in the status quo.
The target's response to this demand, however, is driven by its own views about the future, φB. Since a weak target will capitulate to any equilibrium second-round demand, its first-round calculations weigh the cost of fighting against the benefits of dissuading the challenger from making a “high” second-round demand. In equilibrium, the benefits of building a reputation are large enough to motivate weak targets to fight in the first round if and only if x 1 > p + c B − φB [(C + c A)/2]. Given that the challenger underestimates the target's beliefs about the shadow of the future, the probability that its first threat will be refused by a weak target is expressed by (φB − φA)/2. Adding this to the probability that the target will be tough or moderate (and therefore fight in the first round whenever φA ≤ φB) gives the overall probability of observing compellence failure given disagreement about the likelihood of future crises:
The central result is that the level of disagreement, represented by φB − φA, is positively related to the probability of fighting in the first round. In other words, as the magnitude of disagreement about the future increases, the likelihood of compellence failure increases in tandem. Anything that makes disagreement along these lines more likely thus also increases the likelihood that compellent threats will fail.Footnote 34 From an empirical perspective, the immediate question is: what factors might cause two adversaries to disagree about the probability of future crises between them?Footnote 35
Capabilities, Intentions, and Disagreement About the Future
From a target's perspective, two factors influence the likelihood that it will face future threats: the challenger's capabilities and its intentions. Challengers with extensive power projection capabilities possess the physical ability to threaten many other interests of a target state. Likewise, challengers believed to have expansionist intentions naturally provoke greater anxiety than challengers seen as benign. Disagreement about either factor could cause a challenger and target to hold very different beliefs about the shadow of the future.
Power projection capabilities are largely observable to the target. The ability to project military force depends mostly on tangible factors—advanced weapons platforms (e.g., aircraft carriers or ballistic missiles), technology, logistics equipment, and sheer numbers—rather than hard-to-observe qualities such as leadership and strategy. In addition, power projection depends crucially on geography: states in close proximity to their targets can threaten more possessions, other things being equal, whereas distant challengers pose a smaller risk. Both players therefore have access to much the same information about the challenger's physical ability to threaten a target's possessions in the future. As a result, it is likely that a challenger and target will be able to roughly agree about the challenger's material capacity to initiate future crises.
A challenger's intentions, however, are directly observable only to the challenger itself. Since only the challenger knows whether it wants to acquire more of the target's possessions, the target must infer this information from signals, indices, and other noisy indicators. But a challenger's ability to credibly communicate its motives is inherently limited: clear signals may be unavailable, and a challenger's incentives to conceal its future designs can inhibit the believability of verbal assurances.Footnote 36 The upshot is that a challenger's power projection capabilities are observable to both sides, but its future intentions are not.
This logic implies that it is easier for adversaries to agree about the challenger's physical ability to initiate future crises than its desire to do so, since only the former depends on mutually observable factors. The likelihood that the two sides will reach different conclusions about the probability of future crises therefore depends on the relative importance of the challenger's private intentions in each state's projections about the future.
When a challenger's ability to project military power is minimal, its intentions are largely irrelevant since it lacks the physical ability to make many additional demands anyway. Since this fact is observable to both parties, the two sides in this case are likely to agree that today's threat probably does not foreshadow a cascade of repeated demands. Even if India would have liked to demand more from Portugal than just Goa in 1962, for instance, both sides knew that it lacked the necessary power projection capabilities to do so. Of course, the challenger's initial demand demonstrates that it is capable of making a threat on at least one issue. But military weakness and geographic distance may nevertheless limit its ability to threaten other possessions—particularly if the issue driving the crisis is an overseas interest of the target. When Britain granted Egypt's demand to withdraw from the Suez Canal Zone in 1954, for instance, there was little risk that Egypt would seize on this victory to make threats against the British homeland. Likewise, Indonesia's demands for the island of West Irian in the 1960s probably represented the full extent of Indonesia's ability to threaten Dutch interests. Even when the target is nearby, a challenger's ability to make additional demands against it can be constrained by physical weakness: when Italian leaders relinquished the coastal town of Vlorë to Albania in 1920, for instance, they knew that their smaller neighbor could demand little else. Thus, when a challenger's physical capabilities are minimal, the beliefs φA and φB will tend to converge since they depend mainly on information available to both parties.
The opposite is true, however, when a challenger is physically powerful (or near to the target). In this case, the challenger has the physical capacity to initiate additional crises, so its intentions—which are unobservable to the target—play a larger role in shaping the target's expectations about the future (that is, φB). But since the two sides do not have access to the same information about the challenger's intentions, the odds that they will reach different conclusions—in other words, the chances that φB will exceed φA—multiply. As a result, disagreements about an appropriate value for the target's reputation costs are more likely when the challenger is powerful. As demonstrated earlier, such disagreements also are directly related to the likelihood that compellent threats will fail, since they prevent the challenger from issuing the “correct” equilibrium demand.
The central conclusion is that certain material conditions—namely, military power and geographic proximity—can exacerbate information problems in crises, undermining the chances for successful settlements. They do so by making a challenger's private, future intentions relevant to disputes in the status quo. Although in anarchy there is always some uncertainty about whether a challenger covets a target's other possessions, this uncertainty is immaterial so long as the challenger lacks the means to pursue such aspirations. A challenger's weakness thus does not alter the fact that its future intentions are private; rather, it simply renders this fact irrelevant. When a challenger possesses power projection capabilities, however, its future intentions—and the target's uncertainty about them—become important. A successful threat now requires the challenger and target to reach a common understanding about the challenger's future intentions so that the challenger can accommodate the target's reputation costs. Since these intentions are private, however, disagreements are inevitable, and challengers may demand too much. Moreover, even if a challenger has no future designs against its opponent, merely proclaiming this during a crisis will do little good. A challenger's promise to refrain from making future demands would be believable if it could tie its own hands, but this becomes inherently more difficult as the challenger's power and proximity to the target increase.Footnote 37
Exacerbating the problem is the fact that target states have incentives to exaggerate their fear of future disputes to get better deals in the status quo. If target states could simply declare their beliefs about φ and be believed, then challengers would be able to issue the optimal equilibrium demand. But since targets will be suspected of overstating this value, their only recourse may be to use war as a signal of resolve.
To sum up: extensions to a standard model of crisis bargaining suggest that when targets believe there is a high likelihood of future interactions with their opponent, they will seek to safeguard their reputations by resisting demands that might otherwise be acceptable. Although challengers have incentives to discount their demands to offset the reputation costs of their targets and induce them to acquiesce, the degree to which they can accomplish this depends on the level of congruence in beliefs about the likelihood of future crises. Powerful challengers may not intend to initiate additional disputes, but their inability to commit to future restraint means that target states may nevertheless fear the worst, thus increasing the likelihood that a challenger will underestimate its opponent's anxieties and insufficiently discount its demands.Footnote 38 As a challenger's power projection capabilities expand, this problem becomes more severe since its intentions loom increasingly large in the target's mind but remain difficult to credibly reveal. Thus, other things being equal, a challenger's compellent threats are increasingly likely to fail as its military power and proximity to the target grow.
Reputation and Power in the 1939 Russo-Finnish Crisis
In this section I investigate a specific crisis episode to illustrate the causal mechanisms highlighted by the model described above. I show that Soviet compellent threats against Finland prior to the Winter War of 1939 were hindered by information problems generated by the Soviet Union's overwhelming military power. During the crisis, the Soviet Union's inability to reassure Finland about its future intentions convinced Finnish leaders that war was necessary to dissuade the Soviets from taking a predatory stance toward Finland in the future. Finland thus endured a losing war in part to develop a reputation for stubbornness that would improve its bargaining power in future disputes.
The crisis began brewing in late 1938, when Soviet diplomats sought two primary territorial concessions from Finland: first, an agreement that would allow the Soviets to station naval forces on islands in the Gulf of Finland, and second, a favorable revision of the Soviet-Finnish border on the Karelian isthmus. The Soviet view was that these territories would help the Soviet military defend Leningrad, whose location left it vulnerable to possible German offensives through the Gulf of Finland or through Finland itself. Having grown increasingly unnerved about the growth of German power and the intentions of Adolf Hitler, Soviet dictator Josef Stalin viewed these concessions as a matter of strategic urgency.
When a year of quiet appeals failed to generate results, the Soviets resorted to a series of military threats. During negotiations on 23 October 1939, Foreign Minister Vyacheslav Molotov demanded of his interlocutors “do you want matters to lead to a conflict?”Footnote 39 Then, when talks closed inconclusively on 3 November, Molotov warned that “we civilians can see no further in the matter; now it is the turn of the military to have their say.”Footnote 40 The next day, Stalin himself suggested to Finnish negotiators that they would face the same fate as recently occupied Poland if they refused to compromise.Footnote 41 Finally, during the week leading up to the war, Molotov warned the Finnish ambassador in Moscow that the Soviet government considered the 1934 Russo-Finnish nonaggression pact null and void as a result of a (Soviet-staged) border incident. Despite these warnings, the Finnish negotiating team, led by prominent politicians Väinö Tanner and Juho Paasikivi, continued to refuse Stalin's demands. Once it became clear that verbal threats had failed, the exasperated Soviets invaded Finland. For 105 days, an outgunned Finnish military fought in snow and ice against hundreds of thousands of Soviet troops before suing for peace in March 1940.Footnote 42 The settlement cost the Finns dearly. In the end, Finland's territorial losses far exceeded the Soviet Union's original demands and prompted Finland's bloody revanchist campaign known as the Continuation War, which lasted until 1944.
The failure of Soviet compellent threats in 1939 is puzzling in light of the Soviet Union's extraordinary military advantage over Finland. Even after nearly all of Finland's reserves were mobilized in October 1939, Soviet theater deployments outnumbered Finnish forces by a ratio of 3 to 1 in manpower, 80 to 1 in tanks, 5 to 1 in artillery, and nearly 6 to 1 in aircraft.Footnote 43 Indeed, the Finnish army suffered from substantial neglect during the 1930s and by the end of the decade it had become a tiny, poor, and ill-equipped force. Internal estimates prepared during the crisis suggested that the army had only enough ammunition to support two months of fighting and enough artillery for three weeks.Footnote 44 All of this was well known to Finnish decision makers: Finland's top military officer, General Gustav Mannerheim, noted that “we all knew we were not prepared to meet an attack by a great power.”Footnote 45 Another general advised the civilian leadership during the crisis that “without the slightest doubt we shall lose a war [with the Soviet Union].”Footnote 46
Finland also expected no allied support in fighting the Soviets. As negotiations accelerated in early November 1939, Finland turned down both French and British offers of support—fearing that the two powers sought to use intervention as a pretext to open a military front against StalinFootnote 47—and ruled out the possibility of German assistance.Footnote 48 Instead, Finnish leaders reasoned that their best hope for allied assistance lay with Sweden, whose intervention would carry little risk of bringing a wider war to Finnish ground. But in late October, Tanner's appeal to the Swedish Prime Minister was immediately and explicitly rejected. “You must not reckon with any such possibility,” he was told.Footnote 49
Reputational Motives in Finland's Strategy
The model described above helps shed light on the failure of Soviet compellence in 1939, emphasizing that the sheer magnitude of Soviet power may have hampered its threats by causing Finnish leaders to fear that capitulation would embolden Stalin to exploit them further in the future. Indeed, the historical record suggests that few Finnish leaders believed the territorial stakes themselves were worth a fight; rather, they chose war because they viewed concessions as a first step toward Soviet annexation.
In the language of the bargaining model, Finland's costs for fighting (c B) were high. As a neutral state, Finland wanted no part of the European war that seemed to be approaching, preferring to remain on the sidelines to focus on domestic social and economic objectives.Footnote 50 Finnish leaders placed a high value on the costs of war—in principle, they would be willing to sacrifice much to avoid them. Their aversion to fighting, however, constituted private information to which Soviet leaders were not privy.
Finland's leaders suspected that the 1939 crisis represented a probe of Finnish resolve, after which Stalin would seek additional concessions if the Finns did not exhibit firmness. Indeed, Finnish leaders were privately convinced that Soviet aims far exceeded the moderate demands that Stalin had made.Footnote 51 They knew that Stalin had been eyeing a cluster of Finnish nickel mines in the north and an Arctic port on the Rybachi peninsula, so it was conceivable to them that concessions in the Gulf of Finland and on the Karelian isthmus might lead to further challenges elsewhere. Foreign Minister Eljas Erkko expressed a conviction that “the Soviet aim was a gradual infiltration and penetration of their country” and suggested that the Soviets secretly hoped to re-establish Russia's pre-1917 borders, which encompassed the entirety of Finland.Footnote 52 The Finnish public, once informed of Soviet demands, seized upon a similar rationale: Finland's leading newspaper at the time, the Helsingen Sanomat, editorialized that “acceptance of the demands would mean the collapse of the very basis of our independent existence.”Footnote 53
Two factors exacerbated Finland's anxiety. First, the Soviet Union's massive military power and lengthy border with Finland enabled it to threaten a wide array of Finnish interests if it so chose. The Soviet navy could credibly threaten any part of the Finnish coastline, while ground forces could invade or bombard fronts ranging from Karelia in the south to the Petsamo mines in the far north. As long as Stalin possessed these instruments, the Finns could never be certain that he would not exploit them again in the future.
Second, Soviet behavior elsewhere in Europe struck Finnish leaders as a particularly ominous barometer of Soviet ambitions. In September 1939, the Soviet Union invaded and occupied eastern Poland. In addition, Stalin demanded “mutual assistance pacts” from Estonia, Latvia, and Lithuania, culminating in outright occupations of all three countries. These events, occurring just weeks before the first Finnish negotiators traveled to Moscow, helped marginalize those in the Finnish cabinet who favored concessions and reinforced the conviction of hawkish officials that Stalin had similar designs against Finland. Paasikivi worried that the current crisis was merely “part of a general Soviet military plan for gaining domination over the eastern part of the Baltic.”Footnote 54 So when Stalin offered Tanner and Paasikivi a treaty similar to those recently imposed on the Baltic states, Finnish leaders were suspicious. Even Mannerheim, by far the most conciliatory member of Finland's leadership, feared that “the Soviet Government would soon, as had been the case with Estonia, produce further demands.”Footnote 55 Defense Minister Juho Niukkanen employed a contemporary analogy as well, arguing if Finland did not resist Soviet compellence, “we shall face the fate of Czechoslovakia.”Footnote 56 In this way Soviet behavior elevated Finland's estimate of the likelihood of future crises and reinforced the view that revealing low resolve in the status quo would prove costly in the long run.
Importantly, the model explored above does not predict that reputation-minded targets will stubbornly oppose all demands. Reputations are worth fighting for, but only to a point: even the most reputation-conscious targets will acquiesce if the demand is small enough.Footnote 57 This observation implies that targets should exhibit a willingness to make some concessions even when they believe future crises to be likely. Indeed, Finland proposed a variety of counteroffers in which it would have conceded some of the outer islands in the Gulf of Finland, portions of the Karelian isthmus, and the western Rybachi peninsula in exchange for Soviet compensation.Footnote 58 These counteroffers, though they were rejected, suggest that it would have been possible for the Soviet Union to avoid war by making smaller demands or offering more compensation. Finnish leaders placed a high value on the country's reputation, but they might have been bought off nevertheless.
Disagreements about the Future
A key insight of the crisis-bargaining model is that disagreements about the future (that is, the disparity between φA and φB) provide the mechanism linking reputational incentives with compellence failures. In the model, when a target capitulates to a demand, it forfeits not only the item in dispute but also its reputation for being cost-tolerant. For a deal to be acceptable, targets therefore require some additional compensation to offset the value of their lost reputation. A challenger would ideally like to know the target's true value for its reputation because it could then offer sufficient compensation to secure a peaceful settlement. But challengers know that targets have incentives to exaggerate the shadow of the future (and, by extension, their own reputation costs) to obtain better deals. The model thus suggests that one should observe crisis participants haggling about the probability of future crises, with challengers assuring their opponents that future demands are unlikely and targets trying to evaluate the credibility of those assurances.
Such haggling can be found throughout the bargaining that preceded the Winter War. Throughout the crisis, Finland attempted to achieve a better deal by reiterating its fears about Soviet intentions. Finnish diplomats resisted a number of Soviet demands by explaining their anxiety that a settlement might culminate in a Baltic-style occupation, or at the very least a de facto loss of Finnish sovereignty.Footnote 59 Paradoxically, instead of intimidating Finnish leaders into compliance, Soviet power motivated them to demand a more favorable settlement. As Erkko instructed his team when they departed for talks in Moscow, Finland must “forget that Russia is a great power”—quite contrary to what conventional theories of coercive diplomacy might anticipate.Footnote 60 While Erkko's strategy was based in part on a suspicion that Stalin's threats were bluffs, at the same time he also declared that even if his hunch turned out to be wrong, he nevertheless “would rather let it come to the worst.”Footnote 61
The Soviets were initially receptive to Finnish objections, both revising their demands and offering territorial side payments.Footnote 62 But for the most part they found Finland's anxieties confusing and unpersuasive. “We shall not lift a finger to interfere in your own affairs, nor should we touch your independence,” Stalin assured his interlocutors.Footnote 63 Stalin argued that since he had no additional ambitions to annex Finnish territory, Finland should feel no trepidation about the deal he was offering. Indeed, recently declassified transcripts from Communist Party Central Committee meetings in 1940 suggest that he had no larger designs against Finland and was genuinely puzzled by its intransigence.Footnote 64 In the end, however, the Soviet Union's power worked to its disadvantage, preventing Stalin from credibly assuring Finnish leaders that capitulation in the status quo would not simply provide him with information that he could use against them in the future. Despite his efforts, Stalin could not shake Erkko's conviction that “acceptance of the ‘reasonable and modest’ proposals of today would destroy Finland's ability to resist the immodest demands that were bound to follow tomorrow.”Footnote 65
The Soviet Union's failed compellence attempt against Finland in 1939 illustrates the potentially perverse effects of military power in crisis bargaining. Soviet force projection capabilities, along with Stalin's recent aggressive behavior, led Finnish leaders to believe that by agreeing to concessions, they would embolden Stalin to make additional demands in the future. This logic helps explain why Finnish leaders responded so passionately to Stalin's trivial demands, declaring that “we will not consent to bargain away our independence.” It also helps clarify why they viewed the Winter War—a limited conflict by any definition—as “a war for existence.”Footnote 66 Finnish independence might one day be threatened, Finnish leaders concluded, if they did not resist Soviet compellence in the status quo. Although Soviet leaders significantly attenuated their original demands, the two sides could not agree on a fair “discount” that would compensate Finland for the risk it incurred by sending a signal of weak resolve. Ultimately, Stalin decided that agreement was impossible, and after a series of unheeded Soviet warnings he opted for war.Footnote 67
Conclusion
This article has argued that our understanding of the coercive utility of military power in international crises deserves some reconsideration. While most literature about coercive diplomacy assumes that military power bolsters the effectiveness of compellent threats, analysis of a simple game-theoretic model yields the conclusion that in a world of repeat interactions, one should observe exactly the opposite: other things being equal, powerful states should issue the least effective compellent threats. While exceptional military power allows challengers to threaten severe punishment, it also activates unique information problems that hinder challengers' abilities to locate demands that targets would accept.Footnote 68
Reputational dynamics form the core of this logic. To summarize: challengers would be better off if they could anticipate their adversaries' reputation-building incentives and offset them by making side payments or smaller demands. Since these incentives are closely tied to targets' expectations about future disputes, successful compellence requires that challengers correctly evaluate such expectations and adjust their demands accordingly. As a challenger grows more powerful, however, this becomes more difficult. Adversaries' beliefs about the future become increasingly likely to diverge when challengers are powerful because the challenger's private intentions become more relevant to these beliefs. Since challengers have incentives to underplay the shadow of the future while targets have incentives to overstate it, the two sides may be unable to come to an agreement about how salient the target's reputational interests truly are. Thus, by magnifying the importance of pre-existing information problems, military strength can undermine the effectiveness of compellent threats in international crises.Footnote 69
This argument sheds light on the puzzling observation that compellent threats issued by the United States and other powerful countries seem to have a poor record of success. The logic of reputation-building suggests that the kinds of compellence failures described at the outset of this article are not anomalies but rather represent a systematic pattern. This insight also helps explain why the United States has employed force with increasing frequency even as its military capabilities have grown over time:Footnote 70 its military power may create barriers to negotiated settlements in crises. One should therefore be skeptical of claims that the United States will enjoy an unprecedented ability to threaten opponents into submission in an era of “unipolarity.”Footnote 71
Several testable implications follow from the theoretical argument described here.Footnote 72 First, and most obviously, the theory predicts that militarily powerful states will make less effective compellent threats, on average, since their ability to project power introduces information problems that can cause bargaining to fail. Second, for similar reasons, states in close geographic proximity to their targets will make less effective compellent threats. Third, states known for making frequent compellent threats may find their demands more often refused, since their targets are likely to see significant benefits from building a reputation for cost-tolerance vis-à-vis these states. Each of these conditions can contribute to bargaining failure by contributing to a divergence of views about an inherently unknowable future.
Reputation and War Termination
While this discussion has emphasized how reputation-building dynamics can contribute to the failure of bargaining and the outbreak of war, the logic also contains some surprising implications for our understanding of how wars end. First, it suggests that combatants may continue fighting even if they hold identical beliefs about the balance of power, contrary to Blainey's view that “wars usually end when the fighting nations agree on their relative strength.”Footnote 73 Even if the eventual outcome of the war is already clear to both sides, states may prefer to keep fighting to demonstrate their insensitivity to pain.Footnote 74
Second, when reputation-building is the objective, warfighting states may actually prefer wars that are longer and more costly, since the act of absorbing punishment today could lead to better deals in future crises. Most rationalist theories of war hold that states would rather skip straight to the postwar settlement of a dispute if they could agree about what it should look like, but reputation theory suggests that there is value in publicly enduring the costs of fighting, even if doing so does not produce a better deal in the status quo. Indeed, battlefield losses might paradoxically improve a state's future negotiating power to the extent that they transmit new information about its cost-tolerance.Footnote 75 This finding departs significantly from the common assumption that battlefield losses strictly undermine one's bargaining leverage.Footnote 76
These insights may help explain why wars often do not end when the eventual military result seems clear to both sides. For example, the outcome of the Franco-Prussian War was basically clear after Prussia's victory at Sedan in September 1870, but France continued to fight for months afterward, enduring partial occupation, a siege of its capital city, and several more serious battlefield defeats in the process. One of the reasons the French government was unwilling to sue for peace was that it viewed the war as part of a Prussian campaign for continental dominance, and it was afraid of further aggression after the war ended.Footnote 77 France seemed to prefer paying the costs of fighting—to the point of organizing a guerilla resistance—to show its neighbor that it could not easily be coerced, even though prolonging the fight did not achieve more favorable peace terms (and perhaps led to worse terms) at the end of the war.Footnote 78
Theoretical and Practical Implications
I conclude with three broad observations. First, the argument presented in this article contains an important empirical implication for research about reputations in international crises: even when reputations are important, acquiescing to a compellent threat will not always sully one's reputation for cost-tolerance. The model indicates that challengers in military crises draw new inferences about a target's resolve only when threats are specifically designed to generate them. If a target's reputation for resolve is already strong, then a challenger will be more likely to select a lower-risk strategy that begets minor concessions without actually revealing any new information about the target. In this case, one would observe capitulation to a threat, but the target's reputation would not suffer. Empirical research showing that acquiescence does not consistently harm one's reputation for resolveFootnote 79 therefore should not be taken as evidence that reputations do not impact credibility in crises. The primary effect of a state's reputation may be to prevent a crisis that never happens rather than to influence the outcome of one that does. Reputations “matter,” even if they matter off the equilibrium path.
Second, my argument implies that one should not overstate the degree to which crises must be similar in order for reputation effects to obtain. While skeptics of reputation theory are correct in observing that no two crises are exactly alike, it is inappropriate to infer from this observation that meaningful reputations are rare in international security affairs. The analysis suggests that while crises may differ along many dimensions, they need only raise the specter of military conflict to be “sufficiently alike” to generate reputations for resolve. States that are able to signal that they place a low value on military costs will get better deals whenever military action is the alternative to a negotiated settlement.Footnote 80
Finally, from a practical standpoint, this study suggests that powerful states such as the United States could benefit from finding ways to commit to self-restraint. Coercive diplomatic strategies are more likely to work if challengers can persuade their targets that capitulation will not invite future demands. Reassurances such as President John F. Kennedy's public pledge not to invade Cuba—which helped resolve the missile crisis of 1962—appear more important than previously believed when viewed through the framework of the model above. Measures such as public nonaggression pacts, buffer zones, and arms control agreements could similarly aid the effectiveness of compellent strategies if they can credibly dim the shadow of future exploitation. Successful coercive diplomacy requires not only a sharp sword, but also the ability to sheathe it.
Appendix
Proposition. The strategies described in the text constitute a perfect Bayesian equilibrium.
Proof.
First, conjecture a separating equilibrium for the game Γ in which B's first-round behavior helps A narrow down the range of possible values of c B. In this equilibrium, B accepts A's first-round demand if and only if c B is less than or equal to some cutpoint value Ĉ ∈ [0,C].
To find the equilibrium, begin by locating A's optimal second-round strategy, conditional on B's first-round behavior. Let α serve as a placeholder for a component of A's second-round demand such that x 2 = πp + α. In the second round, B will acquiesce to the demand πp + α if and only if it cannot obtain more by fighting—that is, if π − πp − α ≥ π − πp − c B. This gives the condition c B ≥ α.
If B plays Acq 1, then A knows (by the definition of the proposed equilibrium) that c B must lie along the evenly distributed range [Ĉ,C]. Since B will acquiesce to x 2 = πp + α in the second round if and only if c B ≥ α, then from A's incompletely informed perspective, the probability that B will acquiesce to the second-round demand x 2 = πp + α is equivalent to the probability that c B is less than or equal to α, or (C − α)/(C − Ĉ). A's marginal expected utility for demanding x 2 conditional on B playing Acq 1 is therefore given by (πp + α)[(C − α)/(C − Ĉ)] + (πp − c A)[(α − Ĉ)/(C − Ĉ)].
To find the optimal second-round demand conditional on B playing Acq 1, evaluate the derivative of this term with respect to α, set it equal to 0, and solve for the optimal α, which turns out to be (C − c A)/2. A's optimal second-round demand, given that B acquiesces in the first round, is therefore: x2★ ≡ πp + [(C − c A)/2].Footnote 81
If B instead plays F 1, then A knows that c B lies along the evenly distributed range [0,Ĉ). Again, compute A's expected utility from demanding x 2 = p + α, set the derivative of that function to 0, and solve for the optimal α. This gives (Ĉ − c A)/2. A's optimal second-round demand, given that B plays F 1, is thus x2★ ≡ πp + [(Ĉ − c A)/2].Footnote 82
The next step is now to locate A's optimal first-round demand x 1★, given its uncertainty that a second round will be played. This demand, expressed in terms of Ĉ, must be calibrated so that if it is accepted, then A can be sure that c B ≥ Ĉ. Conversely, if B rejects this demand, then A will know that c B < Ĉ. Calculate x 1★ by supposing that c B = Ĉ and locating the demand that would make B indifferent (and therefore just willing to play Acq 1).
First, specify B's equilibrium behavior in the second round, conditional on its first-round response. If B acquiesces in the first round, it will beget the demand x2★. By playing Acq 2 (if the opportunity arises), it accrues the second-round payoff π − πp − [(C − c A)/2]. On the other hand, by playing F 2, it receives π − πp − c B. Given x2★, B will therefore accept in the second round if and only if c B ≥ (C − c A)/2. Conversely, if B plays F 1, it begets x2★, which it will accept if and only if c B ≥ (Ĉ − c A)/2. Since a separating equilibrium can only exist if Ĉ ≤ (C − c A)/2, two possibilities must be considered for Ĉ: Ĉ = (C − c A)/2 and Ĉ < (C − c A)/2.
If Ĉ = (C − c A)/2, then B will accept A's equilibrium second-round demand regardless of what B played in the first round. B must therefore choose between two scenarios at the outset of the game: F 1,Acq 2 or Acq 1,Acq 2. The demand that makes B indifferent between these two scenarios when c B = Ĉ is calculated by setting the two expected utilities equal and solving for x 1★. The algebra yields x 1★ = p + [(C − c A)/2] − φ[(C + c A)/4].
On the other hand, if Ĉ < (C − c A)/2, then B will reject the demand x2★, so B's choice is between playing F 1,Acq 2 or Acq 1,F 2. The demand that makes B indifferent between these strategy pairs when c B = Ĉ turns out to be x 1★ = p + Ĉ − φ[(Ĉ + c A)/2].
What remains is to show that A prefers to choose its cutpoint Ĉ at (C − c A)/2 rather than somewhere below. Using the assumption that c B is selected from a uniform distribution along [0,C], some ugly algebra yields the following expected utilities: EUA{Γ|[Ĉ = (C − c A)/2]} = (C/4) + (3φC/16) − (c A /2) − (5φc A /8) + (c A2/4C) + (3φc A2/16C) + p + φπp, and EUA{Γ|[Ĉ < (C − c A)/2]} = Ĉ − (φĈ/2) − (Ĉ 2/C) + (3φĈ 2/4C) + (φC/4) − φc A − (Ĉc A /C) + (φĈc A /C) + (φc A2/2C) + p + φπp.
Note that EUA{Γ|[Ĉ < (C − c A)/2]} is increasing as Ĉ approaches (C − c A)/2 from the left. This is shown by first observing that the second derivative of this expression with respect to Ĉ is equal to (3φ − 4)/2C, and since both C ≥ 0 and φ ≥ 0 by restriction, the function must be concave downward. Evaluating the first derivative at 0 thus gives a maximum value for Ĉ: Ĉ = [C(φ − 2) − 2c A(φ − 1)]/(3φ − 4). Now, assuming that Ĉ < (C − c A)/2 at this maximum point yields the expression C + c A < 0, which is false since c A and C are both defined to be non-negative. Thus, by contradiction, it must be the case that the maximum of the function occurs at Ĉ ≥ (C − c A)/2, implying that A's expected-utility function is monotonically increasing as Ĉ increases for all Ĉ < (C − c A)/2.
Next, suppose EUA{Γ|[Ĉ < (C − c A)/2]} = EUA{Γ|[Ĉ = (C − c A)/2]} and solve for Ĉ in order to determine whether A can do better by selecting the separation cutpoint below (C − c A)/2. This equation yields two possible values for Ĉ: (C − c A)/2 and [C(φ − 4) − c A(5φ − 4)]/(6φ − 8). The first solution implies that A is better off when Ĉ = (C − c A)/2 than at any smaller value, since its expected-utility function slopes downward as Ĉ declines from (C − c A)/2. The downward concavity of the function implies that the function's maximum is located beyond (C − c A)/2, so the second solution necessarily violates the condition that Ĉ ≤ (C − c A)/2. The optimal choice is therefore for A to choose Ĉ = (C − c A)/2 and demand x 1★ = p + [(C − c A)/2] − φ[(C + c A)/4]. This completes the separating equilibrium.
The pooling equilibrium is derived simply by evaluating the case where the cutpoint (C − c A)/2 < 0; that is, when c A > C. The separating equilibrium suggests that in this case A will demand x 1 = p + [(C − c A)/2] − φ[(C + c A)/4]. But since c A > C and −φ(C + c A) ≤ 0, p is larger than this demand. Moreover, B is sure to acquiesce to x 1 = p since its expected utility for fighting cannot be greater than 1 − p. A thus demands p, to which all targets acquiesce irrespective of c B.
Given that all types of B acquiesce in the first round when c A > C, the above calculations suggest that A will demand x 2 = πp + [(C − c A)/2]. But since c A > C, πp is larger than this demand. Again, since all targets will acquiesce to x 2 = πp regardless of the true value of c B, then p + [(C − c A)/2] is strictly dominated by πp. Thus, if c A > C, A will demand p in the first round and πp in the second round, and all targets will pool on Acq in both rounds.
