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Over the last quarter century, crisis bargaining has become the prevailing paradigm for the study of war. This textbook presents a concise and approachable overview of the crisis bargaining literature, surveying the canonical formal models in the bargaining approach to war. It begins by considering different explanations for war, then delves into two classes of explanation: commitment problems and incomplete information. This textbook is essential reading for advanced undergraduates, graduates, and researchers alike. Each chapter delves into a specific part of the puzzle, rigorously unravelling the twisted logic that causes wars to begin. More than seventy illuminating figures illustrate the strategic reasoning outlined and more than 100 exercises of graded levels of difficulty help clarify readers' own understanding of the issues. Online resources include an instructor answer key and numerous engaging video lectures.
How can states resolve problems with uncertainty? The most basic way is simply to ask. This chapter shows the unfortunately inherent limitations of such a strategy. If types were to reveal their private information truthfully, weaker types would receive fewer concessions. In turn, those types have an incentive to misrepresent themselves as stronger. Such a desire to take advantage of cheap talk communications continues when mediators are involved, though mediators with their own private information and the right type of bias may see some success.
This appendix describes the implicit function theorem and how it is useful for drawing comparative statics for equilibria that we cannot describe with an explicit functional form.
This chapter explores an underappreciated component of the risk–return trade-off with incomplete information. A central determinant of a state’s willingness to make risky proposals is how much it must overpay weaker types to obtain stronger types’ compliance. When this "peace premium" is large, riskier proposals look more attractive. However, given the right type of uncertainty, increasing the costs of war or decreasing a state’s resolve can counterintuitively increase the probability of war. We also explore a new type of uncertainty: how much value the winner of the war will receive.
This chapter introduces the second general class of bargaining failure: information problems. If one side does not know how costly the other side views war, it may make an onerous demand. Opponents that have low costs reject, leading to war. Although this explanation for conflict is well known, many of its implications are misunderstood. The remainder of the chapter dispels some of them, showing that the probability of war can change as a function of the distribution of power and that more information might cause more conflict.
This chapter introduces the canonical crisis bargaining model. Two states negotiate over a zero-sum good. If they fail to reach an agreement, they fight a costly war. The key insight is that, due to those costs, a range of settlements mutually preferable to war always exists. Thus any good theory of war must first explain why states did not reach one of those negotiated settlements.
This chapter applies the commitment problem logic to situations where it seems unrelated. More specifically, it applies when states can take more of the bargaining good than agreed to, when the size of the bargaining pie depends on pre-war investments, when the bargaining object cannot be cleanly divided, when the parties have risk-acceptant preferences, and when they can incur debt to gain an advantage in war.
This chapter focuses on a particular type of commitment problem known as preventive war. When one side slowly grows more powerful over time, the declining state may prefer fighting a costly war in the present to enduring an efficient but disadvantaged peace later. However, the basic version of this logic only works when states cannot control their future power levels. If they can, and the opponent can monitor those decisions, peace prevails. Moreover, the states may wish to negotiate no power shift whatsoever to avoid paying the costs of weapons.
This chapter introduces the commitment problem. In some cases, states may recognize the existence of mutually preferable settlements. However, one or both may be unable to credibly commit to the conditions necessary to implement those settlements. As a result, the states fight. In particular, this chapter’s focus is on how power dynamics can create such commitment problems.
Previous chapters treated war as a game-ending decision. In practice, negotiations may continue even if the first round of bargaining fails. This chapter covers three different versions of the problem. First, we see that states can learn directly from who wins or loses on the battlefield. Second, states can implicitly learn based on the differential costs of war two types pay. Finally, against multiple bargaining opponents, accepting small proposals can signal weakness for future negotiations. Rather than always lead to more war, it is possible that this instead causes the first proposers to be more generous. Overall, we see that these models are substantially more difficult to work with because of the manipulation of beliefs throughout the rounds of negotiations.
What is generally true about all models of crisis bargaining? Answering a question like this seems daunting because there are infinitely many ways states could negotiate with one another. Fortunately, this chapter introduces a new tool to address the question: mechanism design. We see that types with higher war payoffs will always fight more often than types with lower payoffs, and they will receive better payoffs overall. Meanwhile, it is possible to have negotiations end with guaranteed peace under uncertainty over costs, but no such solution may be possible with uncertainty over power.
This chapter explores the second main source of uncertainty in crisis bargaining: power. At first, the results appear to be superficially similar to how uncertainty over costs works. However, upon deeper inspection, uncertainty over power is harder to mitigate. Even a clever mediator might struggle to solve the problem. Further, states have an incentive to strategically create such uncertainty for their opponents because free riding by not constructing weapons is a tempting choice.