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.

This appendix provides a brief overview of how to calculate and manipulate infinite streams of payoffs.

The problem with cheap talk communication is that it is free to lie in an effort to obtain a better outcome. What if signals were costly instead? This chapter investigates that question from the perspective of military mobilizations. We see that such mobilizations can credibly communicate a state’s resolve because less resolved types pay differential costs to mobilize. Unfortunately, this means that mobilizations are not as useful for revealing private information about the costs of war or a state’s martial effectiveness.

This chapter explains why international researchers prioritize war as a topic of research and summarizes the prevailing theoretical methods used to study conflict. It further narrows the topics that the remainder of the book explores.

This appendix explains the fundamental principles behind mechanism design, why it works, and how we can use the revelation principle to describe what must be true for equilibria within certain classes of games.