In the fall of 1876, Russia queried Germany as to what its position would be if Russia were to go to war with Austria-Hungary. Germany replied, as delicately as it possibly could, that it could not guarantee its neutrality in such an eventuality, and that “a lasting weakening of Austria would be contrary to [German] interests.”Footnote ¹ The German chancellor, Otto von Bismarck, thought that this created a “new situation” in the German-Russian relationship.Footnote ² He meant that Germany had increased Russian expectations about Germany's willingness to go to war on behalf of Austria, and perhaps decreased Russia's appraisal of the extent to which Germany would support Russian aims generally.

According to most theories of information transmission between states, this should have been impossible. Germany communicated its position privately through diplomatic channels. Thus, German elites did not stake their reputation before a domestic audience, nor did their actions carry explicit costs, two commonly recognized mechanisms of information transmission.Footnote ³ Further, Germany's noncommittal statements can hardly be considered to have so engaged its reputation before the Russian and interstate audiences that anyone could have believed Germany significantly less willing to back down for fear of the repercussions of having been caught in a bluff. Theories of information transmission that rely on the staking of bargaining reputations, therefore, also fail to explain the case.Footnote ⁴ Yet Bismarck's appraisal was correct: thereafter, Russia reckoned on German support for Austria-Hungary.Footnote ⁵

In this article, I describe a bargaining model in which states have a richer array of options than the previous literature has allowed. This results in a mechanism of information transmission that provides a convincing explanation for this case, and, I shall argue, represents an essential aspect of interstate diplomacy. The anarchic strategic context can provide less resolved states with a disincentive to misrepresenting their intentions. Very often, when states negotiate over important security concerns, there is a danger that a threat (or other noncooperative behavior) will result in a breach in relations, not merely with respect to the issue at hand, but also with respect to other aspects of the relationship. In such cases, states can send “costless” signals about their intentions. Information is conveyed by threats because states understand the dangers of altering other states' perceptions of their intentions, and yet choose to threaten anyway when they are sufficiently resolved. Alternatively, if foreign policy choices are responsive to perceptions of other states' intentions at all, then explicit threats from one state to another, whether in public or private, can convey information. Thus, this article contributes to the literature on the conditions under which costless diplomatic signals are informative.Footnote ⁶

A second result of the model is a path by which incomplete information can lead to conflict that is different from the mechanism in other models in the literature. War can occur in some equilibria because resolved states decline to communicate their resolve even though they could, and even though this would prevent the war. This can occur when one state is highly resolved, and believes that another is also, but believes that the other state does not believe that the first is highly resolved. In such cases, if the first state were to signal its resolve, there would be a high probability that the other state would prepare for conflict. To avoid this likelihood, the first state declines to convey its resolve to the other. Sometimes, however, the second state would have been willing to comply with the first state's demand in order to avoid war. Thus, in this situation, resolved states mimic the behavior of unresolved states in order to catch the other side unprepared. This contrasts with other signaling models in which it is generally unresolved states that would like to imitate the signals sent by resolved states.

This second point is similar to results derived from other recent models that have begun to expand the range of state options beyond those conceived of in traditional bargaining models. Ritter (Reference Ritter2004, chap. 2) argues that states sometimes make their alliances secret, in spite of the drawbacks from the point of view of deterrence, to prevent potential adversaries from taking countermeasures. Slantchev (n.d.) presents an ultimatum game in which rejected offers lead to conflicts in which each side must choose a level of effort in the fighting. Because the optimal effort of states depends on each side's perception of the strength of the other side, states sometimes have an incentive to make offers in the preconflict stage that hide their true strength. The model below reveals a similar dynamic in the context of costless diplomatic encounters across a wide range of seemingly disparate contexts, from alliance politics to nuclear brinkmanship.

The article has four sections. In the first, I locate the argument in the literature on communication in international relations. In the second, I argue that the strategic options available to threatened states go well beyond the binary choice to comply or not in traditional models of coercion. The third section presents a model that allows states that are threatened to prepare for conflicts and to choose themselves to engage in conflict. When these preparations are effective, informative costless signaling occurs in plausible equilibria. This section discusses the conditions under which signaling can be effective, and under which wars occur that available but unused signals could prevent. A final section discusses implications of the analysis.

COMMUNICATION, CONSTRUCTION, AND DETERRENCE

Social aspects of the human world exist in language, through which they are created, altered, and reified. Within the social realm, some complex constructs, for instance, those that would be identified as sources of cultural difference, are the products of many agents interacting over long periods of time and consequently change only very gradually in general. But other aspects of the social world, such as the “situation” described by Bismarck, change more quickly, and such change is more often intentional. To bring about this sort of change, attempts at communication must succeed in conveying information. That is, they must be believed, at least partially. This article will not address how symbols acquire their meanings or how individuals are initiated into language groups.Footnote ⁷ Rather, I assume for analytical purposes that a shared and unchanging language exists and ask this second question, namely, how it is that attempts at communication by adversaries can convey information.

In particular, I look at one of the most adversarial aspects of relations between states, when one is attempting to coerce another through a threat to use force.Footnote ⁸ Here, more than elsewhere, we expect communication to be difficult because the state making the threat has an incentive to misrepresent its preferences in order to make the threat appear more credible. In such situations, as Jervis (Reference Jervis1970) recognized, analysts distinguish potential sources of information that can be manipulated from those that cannot. The latter can be believed, whereas the former only convey information in certain contexts.

Within the category of information sources that can be manipulated, some messages are credible, even between adversaries, because senders would not want to misrepresent their preferences although they could. When the message causes the sender, in some contingencies, to incur costs as a direct result of sending the message, such messages are called “costly signals.” In game-theoretic terms, the decision to send the message or not has a direct effect on the payoff function of the sender. Perhaps the clearest example from international relations is the decision to build arms. This affects the balance of capabilities directly, but if the arms are costly enough,Footnote ⁹ it may also send a signal to an adversary about the state's intentions.Footnote ¹⁰ The adversary may conclude that a less resolved state would be unwilling to pay those costs.Footnote ¹¹

But messages need not be associated with direct costs for there to be disincentives to lie, and thus for the message to enable to the receiver to learn something from it. Whether such disincentives exist depends on the strategic context. Suppose, for instance, that an employer wants to give a high-paying position to an experienced applicant and a low-paying position to an inexperienced one. If there is no way to verify whether a candidate is telling the truth, the candidate may have a hard time convincing the employer that he or she deserves the high-paying position. On the other hand, if the high-paying position is for a pilot and the low-paying one for a flight steward, the candidate's statements about his or her hours of flight experience may well be at least partially informative. Misrepresenting qualifications in this case may result in his or her flying planes, which for the inexperienced may result in a crash that has negative consequences for both employer and employee. In this employment example, therefore, the two sides have interests in common; communication of private information may be possible. In the game-theoretic literature, such signals are called costless because the actions available to agents and the payoffs associated with material outcomes are all unchanged no matter which message is sent.Footnote ¹²

Models in the economics literature show that the maximal degree of precision of credible costless messages increases as the interests of sender and receiver grow more aligned.Footnote ¹³ In two-player games, when relationships are zero-sum, no “cheap talk” communication is possible at all. Understanding the degree to which interests are aligned, however, turns out to be far more difficult than it appears at first glance.Footnote ¹⁴

Many scholars of international relations have concluded that relations between states are too adversarial for costless communication to occur. For instance, Schelling noted that “words are cheap, not inherently credible when they emanate from an adversary. . . .”Footnote ¹⁵ Fearon, careful not to overstate the case, argued that “it remains unclear whether cheap talk is important in international disputes. . . . His work as a whole suggests, however, that, “costless signals. . . have no effect” on international outcomes.Footnote ¹⁶ Many other scholars have followed their lead. I show below that the preferences of state adversaries are in fact sometimes sufficiently aligned to allow costless communication to occur.

This distinction between costly and costless signals may seem merely technical, with little substantive importance. This is not the case. On it hinges the question of whether diplomacy, particularly that practiced by leaders behind closed doors, can play a role in determining the course of events in a rationalist framework. Macro-level theories of the international system have generally claimed to explain international events without reference to diplomatic communication.Footnote ¹⁷ This orientation has received support from micro-level theorizing of conflict processes, which has suggested (if not stated outright) that only directly costly activities such as mobilizing troops, building arms, and creating “backdown costs” can convey information. As a result, international relations scholarship has neglected the study of the role of private diplomatic communications, both theoretically and empirically.

There are important exceptions to this characterization of the literature, however, and recent scholarship has shown a renewed interest in the mechanisms of private diplomacy. Sartori (Reference Sartori2002; Reference Sartori2005) has demonstrated that private diplomatic communications can be made credible by the desire of states to maintain a bargaining reputation, which makes them hesitant to send misleading signals for fear of being caught in a bluff.Footnote ¹⁸ Guisinger and Smith (Reference Guisinger and Smith2002) combine two strains of the literature to show that in the presence of a reputational mechanism along the lines of Sartori's, democratic selection of leaders results in an endogenous additional disincentive against bluffing. Kurizaki (Reference Kurizaki2004) shows that if a publicly threatened state will lose face by backing down, then it is sometimes optimal for states to make private threats. Such threats do not increase the probability that the threatened state assigns to the threatener following through, but neither do these private threats cause that probability to go to zero.Footnote ¹⁹ Kydd (Reference Kydd2003) presents a cheap-talk model of third-party mediation.Footnote ²⁰

Earlier work describes several other mechanisms of private diplomacy.Footnote ²¹ Schelling (Reference Schelling1966, Reference Schelling1980) argued that threats sometimes risk an undesired event that neither side directly controls, which causes the threats to convey information. The essence of brinkmanship is that when one climber who is roped to another moves closer to the edge, he or she may slip. By demonstrating a willingness to slip, the climber conveys information about his or her resolve in the issue being negotiated.Footnote ²² Schelling's analysis focuses on how engaging in limited forms of conflict can constitute an implicit threat because it demonstrates a willingness to risk even more costly conflict. Private threats may have a similar effect, however, in that they delay resolution of the issue and create a crisis atmosphere in which conflict may be more likely. Schelling's work bears important similarities to the analysis to follow. Here, however, the emphasis will be on the intentional action of actors rather than the partly exogenous danger of sliding off a cliff and on the implications of including the option to prepare in models of the conflict process. The analysis to follow also makes it clear that some of the dynamics of engaging in limited conflict are equally germane to costless signals and thus to private diplomacy.Footnote ²³

Of these mechanisms for private information transmission, the staking of bargaining reputations has received the most attention. Despite some scholarship that argues to the contrary, I believe the diplomatic–historical record supports the proposition that the maintenance of a reputation for being true to one's commitments has been an important force in international affairs.Footnote ²⁴ As in the case of Germany's tacit threat to Russia in 1876, mentioned above, however, important information is often conveyed by costless diplomacy that cannot be explained by reputational dynamics. In this case and in many others, in making a threat, policy-makers on both sides were not primarily concerned with bargaining reputation. Rather, Germany worried about consequences that would follow if, as it expected, its private threat were found credible. Further, in many cases where reputations may appear to have been staked, the mechanism I propose here represents an alternative and sometimes more plausible explanation of communication.

The model in this article contributes to this growing literature by providing a new mechanism of information transmission between states that applies to certain systemic contexts and appeals neither to the costliness of the signal, nor to bargaining reputation. The theory applies equally to messages conveyed in public and in private. It also demonstrates that a similar signaling mechanism is at work in seemingly diverse strategic contexts, such as nuclear brinkmanship and alliance bargaining.

THE STRATEGIC CONTEXT OF ANARCHY

In prominent models in the international relations literature, the strategic options of the target of a threat are limited: it can stand firm or concede. This conceptualization does not correspond to the options and incentives of states in the anarchic international context. If a state comes to believe it cannot achieve its key strategic aims through its current relationship with another state, it may choose to alter that relationship. In particular, rather than merely deciding whether or not to back down, threatened states must decide how to prepare for conflict if they believe a breach with a threatening state is imminent. In such cases, states often reorient their security policies in order to drain resources from the threatening state, and they also tend to form new alliances that are contrary to the threatening state's security interests. In addition, when the target of a threat believes future conflict is more likely, it will sometimes choose to increase arms production, mobilize troops, or strike first. These decisions are often made before the threatening state chooses to back down or follow through on its threat and have consequences whether or not the states involved ultimately go to war.Footnote ²⁵

To illustrate the strategic choices available to Targets, consider the responses of U.S. President Kennedy and Soviet Premier Khrushchev to each other's threats in their June 1961 meeting. Put simply, each threatened to escalate to war if the other did not accept a settlement of the Berlin question favorable to his side. Following the meeting, Khrushchev responded by adopting a new set of policies designed to drain the resources of the United States. On August 1, he “approved most of a KGB plan to create ‘a situation in various areas of the world that would favor the dispersion of attention and resources by the United States and their satellites, and would tie them down during the settlement of a German peace treaty and West Berlin.”'Footnote ²⁶ For his part, hard as it is to imagine today, Kennedy began to take the idea of a nuclear first strike more seriously. He told the Joint Chiefs of Staff that “Berlin developments may confront us with a situation where we may desire to take the initiative in the escalation of conflict from the local to the general [nuclear] war level.”Footnote ²⁷ Thus, because both leaders were unwilling to back down, they considered or adopted policies to prepare for a conflict they thought might be imminent.

Alternatively, consider the Japanese strategic calculus in 1941. In November of that year, the United States demanded that Japan withdraw from China. This amounted to “surrendering her position as a power in the Far East.”Footnote ²⁸ Japan was unwilling to accede to U.S. demands, and, precisely because it found U.S. threats credible, decided to take radical action to prepare for the coming conflict. In the hope of demonstrating its resolve to resist, and of engaging in only a limited war with the United States, Japan opted to destroy the offensive capability of the U.S. fleet at Pearl Harbor.Footnote ²⁹

The history of international relations is full of examples of states responding to diplomatic pressure with actions that go well beyond a simple refusal to comply with a demand. In fact, where important questions of security are concerned, simply declining to comply with demands is likely the exception rather than the rule. The Japanese response to U.S., British, and Dutch policy in 1941 was exceptional only in scale and decisiveness.

In response to Austrian threats during the Crimean War, Russia took actions it would not have taken otherwise. These included colluding with France and Sardinia to strip Austria of northern Italy, tipping the balance in Germany in favor of Prussia, permitting the revolution in Hungary that resulted in the Austro-Hungarian Ausgleich (instead of assisting in suppressing the Hungarians as Russia had before the war), and declining to renew generous offers of Russo-Austrian cooperation in the Balkans, leading to drastically increased security competition in the region between the two countries.Footnote ³⁰ More speculatively, but with some justice, the historian Norman Rich argues that the Austrian threats during the Crimean War resulted in “a bitter hostility that was to culminate in war in 1914, the destruction of both imperial houses, and the liquidation of the Habsburg Empire.”Footnote ³¹

A particularly common response to dissatisfaction with another country's conduct of foreign policy and its perceived hostile intentions is the realigning of alliance commitments. In 1864, for instance, Napoleon III wished to use a European conference to revise the post–Napoleonic Wars settlement of 1815. When Britain, with which France was closely aligned, refused to support a conference, Napoleon was explicit: “So it seems we shall have no Congress. Well! I shall have to change my alliances.” With that, the alignment between the two countries ended.Footnote ³²

The danger of a great power realignment resulting from a general breach in Russo-German relations is also the explanation for the information conveyed by Germany's statements in 1876 discussed above. Both sides understood that even a tacit threat from Germany might lead Russia to form an alliance with France, Germany's arch rival since the Franco-Prussian war six years before. The fact that Germany understood the danger, and yet chose to tacitly threaten anyway, meant that Germany had effectively communicated its resolve to defend Austria-Hungary.Footnote ³³

To fix ideas, and to see the relationship between preparation for conflict and communication, consider the following stylized examples of international contexts in which costless communication is possible. The model presented in the next section is designed to represent these situations in a stylized way. As these narratives make clear, signaling dynamics can be similar in seemingly diverse strategic contexts.

Example 1 (External Balancing). A conflict arises between two states, a Deterrer and a Target, over a specific issue. In order to get its way, the Deterrer would like to signal its willingness to go to war over the issue to the Target. The Deterrer knows, however, that if the issue is particularly important to the Target, the latter may form an alliance with a third country in order to get its way or prepare for a possible conflict. The Target would prefer not to make the concessions to the third state required to get an agreement, and the new alliance is also likely to have a negative effect on the Deterrer's security position, especially if the third country is already hostile to the Deterrer. Threat-making therefore has both an advantage and a drawback. The advantage is the increased likelihood that the Target state will concede the issue to the Deterrer; the drawback is the possibility that the Target will “balance” against the Deterrer by forming a hostile alliance. As has been mentioned, this was the principal concern in German relations with Russia after the Franco-Prussian war. Deterrers for whom the issue is not sufficiently important are unwilling to incur the risk of such a breach in relations by making a threat. When the Target state observes a threat, therefore, it learns the issue is relatively important to the threatening state.

Example 2 (Internal Balancing). As the name implies, this scenario is similar to the last, except that the principle strategic option of the Target (the threatening state's principal concern) is to transfer resources to its military sector in order, one day, to resist the demands of the threatening state. The timing of China's decision in the 1950s to devote enormous diplomatic and material resources to the pursuit of nuclear weapons, for instance, may have been partly a result of U.S. threats in the first and second Taiwan Strait Crises. Because such arms production alters the future bargaining relationship between the nations, internal balancing will often constitute a significant long-term drawback to threat-making.

Example 3 (First Strike). If a Deterrer threatens a Target, the military and strategic context may be such that if the Target is unwilling to back down and believes the Deterring state is also sufficiently unlikely to back down, the Target's best option is to strike first. This was the situation for Japan in 1941. It was also a worry for U.S. President Kennedy during the Cuban missile crisis. He recognized that a U.S. threat to destroy the missiles in Cuba in four days could result in a Soviet threat to take action in three days, as well as further escalations that could result in nuclear war in that time frame.Footnote ³⁴ In such military-strategic contexts, therefore, threat-making once again involves a trade-off similar to that in Examples 1 and 2. Threats increase the chance that a state gets what it wants with respect to the issue at hand, but can also create a danger that the threatened side will begin an unwanted military conflict. Once again, the willingness of the Deterrer to incur such a risk can cause the threat to convey information to the Target.

Example 4 (Too Costly Deterrence). Faced with a threat, the Target might consider adopting policies that would deter the threatening state from attacking. Such activities, for instance mobilizing forces on a border, may be too costly to sustain for long. Rather than maintain a high level of preparation, therefore, the Target state might prefer to go to war. Powell (Reference Powell1993) analyzes a strategic context that leads to a similar dynamic. From the perspective of diplomatic signaling, if we think of the Target's decision as preceding the Deterrer's decision to go to war or back down, the danger of such an outcome plays a similar role to the risk of a first strike in Example 3.

Example 5 (Resource Drain). Other reactions that states may have to threats also have long-term consequences for the threatening state. As the Soviet Union did following the Vienna meeting, for instance, a state may choose to drain the resources of another state in order to get its way on a particular issue. As in Examples 1–4, the risk that a threatened state will adopt such a course provides a disincentive to less resolved states to signal their willingness to engage in conflict over such a contentious issue, making communication possible.

Example 6 (Mobilization). When a threatened state declines to back down and believes conflict likely, it may elect to mobilize its troops. With the cost of the mobilization paid, the choice to go to war looks more attractive to the mobilized state than it had previously.Footnote ³⁵ If we allow for the possibility that the mobilized state will go to war, we once again have a tradeoff for states that consider threat-making, and this again results in the possibility of informative signals.

In each of these narratives, the decisions the Target of a threat takes when it means to resist the deterring (or compelling) state's demands have a negative impact on the Deterrer's utility. If the Target chooses either internal or external balancing, the Deterrer's utility will be negatively affected even if it chooses not to go to war. This is true when the increased capabilities of the Target increase the likelihood that the Target will decide to go to war itself, and may also be true when the Target will not contemplate war in the near term. In the context of Russo–German relations in 1876, Bismarck was explicit on this point. Even a tacit German threat to Russia, he argued in one foreign policy circular, “could induce [the Tsar] to conclude flawed resolutions and alliances that would be very disadvantageous for both sides.”Footnote ³⁶ A Franco-Russian alliance would have had consequences for Germany whether or not the Germans backed down in 1876.Footnote ³⁷

Internal and external balancing on the part of a Target negatively affects the Deterrer's expected utility from peace because it changes the balance of power between them. If the two countries are involved in another crisis in the future, the weaker relative position of the Deterrer will usually mean that it is less likely to get its way and more likely to fare badly if conflict should actually break out. Thus, if future crises are of the sort described here or, for example, in Fearon (Reference Fearon1994, Reference Fearon1997, Reference Fearon1998), Schultz (Reference Schultz1998, Reference Schultz2001) or Slanchev (Reference Slanchev2005), the Deterrer's expected future utility decreases in the capabilities of its adversary.Footnote ³⁸ Although there may be some contexts in which states are indifferent to the increasing capabilities of an adversary, they will more often view such developments with understandable concern.

In the model described below, we allow for the possibility that the Target of a threat, having made costly preparations for war, might choose to begin one. This results in a concrete risk to the coercing state of appearing to menace the other state. Even if the coercing state backs down, the other state may make preparations for war and choose to fight one. More generally, however, we might think of the preparations of the Target negatively affecting the coercing state's utility because of the effect of preparations on the balance of power, even when the coercing state backs down and the sides are not in immediate conflict.

COMMUNICATION IN ANARCHY

We now turn to a formal model of coercion in which we allow for the possibility that threatened states may decide to take actions that go beyond standing firm or backing down. In the model, there are two players, a Deterrer or threatening state and a Target or threatened state. The players are indexed by i ∈ I ≡ {d, t}.

The model below is different from previous models in the international relations literature in two important respects. First, the Target can chose to prepare for conflict when it believes it is sufficiently likely, or reorient its foreign policy in other ways that are hostile to the interests of the threatening state. If the Deterrer takes a threatening posture, and if the Target's costs of war are sufficiently low relative to the importance of the issue in question, the Target may be convinced to take these sorts of measures. Second, in addition to the Deterrer having the option to attack the Target, the Target has the opportunity to attack the Deterrer. Having prepared for war, the Target may opt for it even if the Deterrer does not. Because the Target's actions may lead to an outcome that is even worse for an unresolved Deterrer than the peaceful outcome where the Target is undeterred, a resolved Deterrer has an incentive to make threats vis-a-vis a particular issue that less resolved states would be unwilling to make. As I show below, this dynamic causes threats to be meaningful even though no direct cost is associated with making them. One general implication of the model is therefore that if states respond at all to perceptions of other states' intentions in formulating foreign policy, then a verbal threat made by one state against another, whether in public or private, can convey information.

Following other models in the international relations literature, we shall suppose there is a bargaining space X ≡ [0, 1] such that the Deterrer prefers outcomes closer to 1 and the Target outcomes closer to 0. The status quo at the beginning of the game is s ∈ X. Players have von Neumann–Morgenstern utility functions defined over outcomes in the bargaining space, x ∈ X, and whatever costs of fighting and preparation for conflict the players pay, c _i. Specifically;

and

Thus, players have risk-neutral preferences over outcomes in the bargaining space. We assume this because it simplifies the exposition without substantively altering the key points of the analysis. The costs players pay in the game, c _d and c _t, will be defined below as functions of other variables to reflect the outcomes of player actions during the game, so that, for instance, the players do not pay a cost of conflict when no war is fought. (They may still pay a cost of preparing for conflict, however.)

Figure 1 depicts the stages of the game. It begins with the Deterrer's attempt to influence the Target by sending a costless signal. Whatever message the Deterrer sends, the game that follows is precisely the same; action sets, the sequence of moves, and player utilities are all unchanged. If the initial communication stage is important at all, therefore, it is only because the Deterrer's message affects the Target's beliefs about the Deterrer's intentions. This is possible in equilibrium when the Deterrer is aware of the conclusions the Target will draw from a particular messaging strategy of the Deterrer (and thus also aware of how these conclusions will likely affect its actions), and yet the Deterrer's best option is nevertheless to use that very messaging strategy. We restrict attention to the Deterrer's decision to threaten or not, which we represent by the message m ∈ M ≡ {0, 1}. We shall interpret m = 1 as a promise to take violent action if the Target takes a particular action, as well as a promise not to take violent action in the event the Target cooperates.

FIGURE 1.

Stages of the Game

In the second stage, the Target has two decisions to make: whether to take the action in question or not (choosing a ₁ ∈ A ₁ ≡ {0, 1}), and whether to prepare for conflict (choosing a ₂ ∈ A ₂ ≡ {0, 1}). If the Target takes the action, setting a ₁ = 1, it unilaterally moves the status quo to s − ε, toward its ideal point, where ε ∈ (0, s]. If the sides remain at peace, this will then be the bargaining outcome. Then, in the third stage, the Deterrer and Target decide whether or not to go to war by choosing r _i ∈ R _i ≡ {0, 1}, where 1 represents conflict initiation. First, the Deterrer chooses r _d. If r _d = 1, conflict occurs; if not, the Target chooses r _t. War occurs if either side opts to begin one; both sides must choose peace to obtain that outcome. We let r represent an indicator variable that equals 1 when the sides go to war and 0 otherwise. Thus, r = 1 if and only if r _i = 1 for some i.

If the sides should fight a war, the Deterrer will win the war with common knowledge probability p(a ₂), and is then able to choose its ideal outcome in the bargaining range X. Similarly, if the Target should win the war, it may choose its ideal bargaining outcome. We assume that one of the two sides will win the war. When the Target prepares, the chances that it wins a war may increase: 1 − p(1) ≥ 1 − p(0) ⇔ p(0) ≥ p(1).

We shall model the Target's costs of war and preparation as consisting of several components. If the sides go to war, the Target's war costs are , where and η_t is private information of the Target. If the Target chooses to prepare, it incurs some preparation costs, k _t ≥ 0, whether or not a war is fought, but reduces its costs of conflict by . Thus, preparations imply an increase in the sunk costs that the Target pays whether or not it goes to war and a decrease in the variable costs associated with the conflict itself. (We make no assumption about the net effect of preparations on the overall cost of conflict.) Thus,

We take a similar approach to modeling the Deterrer's costs, but we suppose the Deterrer has already made any relevant preparations for conflict and do not model the Deterrer's choice of preparations explicitly. For simplicity, we suppose the Target's preparations do not affect the Deterrer's costs of conflict—only its probability of victory. Thus,

where , and η_d is private information of the Deterrer. Both sources of private information are independently distributed according to the continuous, strictly increasing, common knowledge distribution functions Φ_ηi.

Thus, the Deterrer's utility depends on the bargaining outcome, whether the players go to war, and the Deterrer's type, whereas the Target's utility depends on those same factors and also on whether or not the Target chooses to prepare. Therefore, we shall write the players' utility functions as u _d(x, r, η_d): X × R × → and u _t(x, r, η_t, a ₂): X × R × × A ₂ → .Footnote ³⁹ Substituting the cost functions into the player utility functions yields the following utilities for peace:

Similarly, the players' expected utilities for war areFootnote ⁴⁰

The formal structure of the game is shown in Figure 2. Whichever choice the Deterrer makes in the first stage, the Target has the four Stage 2 options shown in the figure. Whichever of these the Target opts for, the same Stage 3 structure shown follows. As the figure shows, the players' utilities over the Stage 3 terminal node outcomes depend on the Target's Stage 2 choice. The full game tree, therefore, has 24 terminal nodes (2 Deterrer options in the first stage × 4 Target options in the second stage × 3 terminal nodes in each Stage 3 branch).

FIGURE 2.

Formal Structure

To make the signaling problem interesting, we shall make several assumptions about payoffs. First, we assume the Deterrer prefers not to go to war when the Target complies with its wishes by not taking the action, and that there is a possibility the Deterrer would be willing to fight if the Target did not prepare and took the action in question and a possibility the Deterrer would not be willing to fight in this case. This is equivalent to

(1)

Second, we assume the Target prefers peace when it takes the action in question and does not prepare to its most preferred war outcome and that there is a possibility the Target would prefer a prepared war to accepting the initial status quo and a possibility the Target prefers the initial status quo to a prepared war. This is equivalent to

(2)

Similarly to other models of coercion, these assumptions imply that the Deterrer's most preferred outcome occurs when the Target complies with the Deterrer's wishes by not taking the action in question (and also not attacking the Deterrer). The Target's most preferred outcome occurs when it takes the action in question, does not prepare for conflict, and the Deterrer does not attack. Players are willing to go to war when they consider the costs of war to be low relative to their evaluation of the issues at stake and their chances of victory.Footnote ⁴¹ An example of parameters satisfying these assumptions is shown in Figure 3. The figure also represents the model in terms similar to those used in Fearon (Reference Fearon1995) and can usefully be compared to Figure 1 of that paper.

FIGURE 3.

Player Utilities Satisfying Model Assumptions

The preparations of the Target may or may not have an effect on the Target's costs of conflict and the players' probability of victory. We shall say that preparations are effective if and only if k _t > 0, p(0) > p(1), and [(1−p(1))−(1−p(0))] > k _t−β_t. The last condition states that the Target prefers a prepared to an unprepared war, or in other words, that the overall increase in the Target's costs as a result of preparation (if preparing does involve a net increase in costs) must be outweighed by the benefit of the increased likelihood of victory. We shall say preparations are ineffective if k _t = β_t = 0 and p(0) = p(1).Footnote ⁴² Note that in Figure 3, preparations are effective.

Discussion of Equilibrium Dynamics

We can understand comparative statics in the model by considering the example of an influential equilibrium discussed above. The effect on signaling dynamics of the players' beliefs about each other's willingness to fight is shown in Figure 4. This figure and others that follow were generated through numerical simulations of the model. Recall that in our example, the players' costs of conflict are drawn from uniform distributions over . We can model shifts in the players' beliefs about each other's resolve by shifts in and . In Figure 4, is on the vertical axis and is on the horizontal axis. Thus, as we move rightward in the Figure, the Deterrer is less convinced of the Target's resolve, and as we move upward, the Target is less convinced of the Deterrer's resolve (before a signal is sent).

FIGURE 4.

Equilibrium Signaling Properties

When the Deterrer is too much or too little convinced of the Target's resolve (very low or very high ), or when the Target is too convinced of the Deterrer's resolve (low ), influential signaling is impossible. In the middle of the figure are the two ranges where influential signaling is possible, but there are interesting differences in the dynamics of signaling and conflict between these two ranges. In both, the threats of the Deterrer convince the Target that the Deterrer is more likely to be willing to fight over the issue in question than the Target had previously thought. In the rightmost semiseparating equilibrium, however, the Target knows for sure when the Deterrer declines to threaten that the Deterrer will not fight over the issue. In the leftmost semiseparating equilibrium, this is not the case. There, the Deterrer sometimes, but not always, misrepresents itself as less resolved than it actually is in order to catch the Target unprepared.

Figure 5 provides us with a closer look at the signaling properties when is held fixed at 0.75, as in the example of the previous section. is on the horizontal axis, as in Figure 4. Within the middle range where influential signaling is possible, the more convinced the Deterrer is of the Target's resolve (the lower ), the more informative is the Deterrer's signal. When increases, the probability that the Target complies with the Deterrer's demand increases, which causes the probability that the Deterrer is willing to threaten to increase as well, and the signaling value of a threat to decline. Thus, when = 0.775 a threat causes the Target's evaluation of the likelihood the Deterrer would fight to jump from 14% to 49%. When = 0.875, in contrast, a threat causes the Target's evaluation of Deterrer resolve to change only from 14% to 26%.

FIGURE 5.

Effectiveness of the Signal and Likelihood of Surprise

When increases enough, the change in the Target's beliefs as a result of the Deterrer's signal suddenly falls discontinuously to zero as signaling becomes impossible. This can be seen on the right-hand side of Figure 5. The reason is complex and relates to the interaction of a number of factors. As increases and the Target comes to believe that the Deterrer is less likely to follow through on a threat (because the Target knows that the Deterrer knows that the Target is itself less likely to be willing to fight over the issue and thus the Deterrer has less to lose from making a threat), Target types in the middle of the range of cost types have a new optimal strategy. Even if the Target did find the Deterrer's signal to be somewhat informative, rather than low Target cost types preparing and then fighting and high Target cost types backing down, Target cost types in the middle of the η_t range would prefer to take the action in question without preparing at all. They find the chance that the Deterrer is willing to fight to be too low to justify the expense of preparation, but neither are they deterred from taking the action in question. As a result of the change in the Target's strategy, the Deterrer would have both less to fear from threatening and less to gain. The former effect dominates the latter, causing the Deterrer to be even more willing to make threats, which in turn would cause even more Target types to prefer taking the action in question without preparation, and so on, with the result that influential signaling is impossible.

When the Deterrer believes it relatively likely that the Target will not back down over the issue, so that is low, but still in the range where influential signaling possible, surprise attacks (i.e., attacks not preceded by a threat) occur in equilibrium. When the Deterrer's costs of conflict are very low, it prefers not to threaten the Target at all in order to be able to attack the Target when the Target is unprepared. In such cases, as we saw in our analysis of noninfluential equilibria and diplomatically avoidable wars, conflict can occur in equilibrium because the Deterrer is unwilling to risk communicating its resolve. A signal exists that the Deterrer could send that would result in compliance and avoid the need for either side to go to war, but because the Deterrer does not know that the Target would comply with a demand if the Target knew the threat were credible, the Deterrer declines to send the signal.

In traditional crisis bargaining models, war can often occur because the Deterrer does not have the means available to communicate its resolve.Footnote ⁴⁸ As we saw above, in diplomatically avoidable wars, the Deterrer has the ability to communicate but chooses instead to catch the Target unprepared.Footnote ⁴⁹ Instead of the weak Deterrer types mimicking the strong, in such cases, the strong pretend to be weak because they believe the Target is unlikely to back down even if it knew the Deterrer were in earnest.

Unlike the situation in the noninfluential equilibrium of Proposition 3, however, in this example, diplomatically avoidable wars and influential signaling coexist in a single equilibrium. Deterrer's adopt four different approaches, depending on their level of resolve. The very most resolved Deterrers are unwilling to risk Target preparations and choose to use a surprise attack. They will attack an unprepared Target without first attempting to coerce through a threat. The next most resolved Deterrers make threats that they will follow through on if the Target does not acquiesce. Deterrer types that are slightly less resolved than these will make threats they would later be unwilling to prosecute and, finally, the least resolved Deterrer types make no threat at all and later choose not to attack.

Because the likelihood of a surprise attack increases as decreases, the lower , the less the Target can learn from the Deterrer's decision to decline to threaten. When = 0.775, for instance, the Target's evaluation of Deterrer resolve declines only slightly when the Deterrer declines to threaten: from 14% to 13%. When = 0.875, the Target's evaluation of the likelihood of Deterrer resolve falls from 14% to 0%. Thus, when there is a high probability that the Target is highly resolved, the Target learns the most from a threat; but when there is a high probability that the Target is unresolved, it learns the most when the Deterrer declines to threaten.

As can be seen on the left-hand side of Figure 5, at the extreme, when the Deterrer believes the Target very unlikely to back down in response to a threat, influential signaling is impossible because the incentive for a resolved Deterrer to attempt to surprise the Target is too great. When the Deterrer is highly resolved, it always prefers that the Target not know this. Thus, in this region, the Deterrer never threatens, in the sense that low-cost Deterrer types have an incentive to imitate high-cost types.Footnote ⁵⁰ Once again, diplomatically avoidable wars can occur in equilibrium.

The existence of a communication mechanism lowers the probability of war in general. In the parameterization discussed here, when none exists, the probability of war is 14% for all values of shown in Figure 6. The reason is that when the Deterrer cannot affect the Target's beliefs, the Target's optimal strategy for all values of η_t is to take the action in question without preparing. Thus, war occurs if and only if the Deterrer prefers to fight one, given that the Target has taken the action and not prepared.

FIGURE 6.

Probability of War

When a communication mechanism exists, the probability of war is reduced over parameter ranges where influential signaling is possible, as Figure 6 illustrates. As we approach the left border of the range where influential equilibria exist from the right, the probability of war is arbitrarily close to the probability of war when no communication mechanism exists. This is so for two reasons. First, even though threats are very informative, as shown on the left-hand side of Figure 5, they are rarely used, as can be seen from the upward-sloping line in Figure 6. When the Deterrer is resolved, it often prefers the gamble of a surprise attack to the gamble of diplomatic signaling. Second, when is relatively low, there is a low probability that the Target is willing to back down. As increases, so that the Target is more likely to be a high-cost type, even though threats are less informative, they become more used, surprise attacks decline, and the Target is more likely to be willing to back down, with the result that the probability of conflict decreases. When = 0.875, for instance, the probability of war is 4%, less than one-third of what it would be in the absence of a communication mechanism.

When increases enough so that signaling becomes impossible, however, the probability of war jumps discontinuously back from 4% to 14% for the reason given above. If we were to consider parameterizations where was much higher, increases in would again cause the probability of war to decline because Targets for whom war was extremely costly would either decline to take the action in question or make preparations such that the Deterrer would itself be deterred from initiating a conflict. Thus, communication results in a nonmonotonic relationship between the probability that the sides are willing to fight and the probability of war.