Alignment Patterns, Crisis Bargaining, and Extended Deterrence: A Game-Theoretic Analysis

To explore the impact of alignment patterns in a rudimentary state system, we develop and analyze the Tripartite Crisis Game, a three-person game among Challenger, Defender, and Protégé. This model captures some of the tensions implicit in the "Alliance" and "Adversary" games, two related but theoretically isolated models due to Snyder. Our analysis enables us to delineate and explore the circumstances that give rise to the "deterrence versus restraint" dilemma. It also provides an answer to Fearon's empirical puzzle: when convincing commitments are possible, why are halfhearted signals sometimes sent?
Our most surprising result concerns the impact of Protégé's threat on Challenger's optimal behavior. When Challenger is willing to fight to back up its demand, but is nonetheless only weakly or moderately motivated, Protégé's threat to realign—though directed at Defender— can dissuade Challenger from initiating a crisis. But when Challenger is willing to fight and stands to gain a great deal, Protégé's threat may actually prompt Challenger to make a demand. Our analysis uncovers this unexpected pattern of behavior and suggests when it occurs. That Protégé's threat to realign sometimes bolsters deterrence, and sometimes undermines it, has implications for the selection bias issue in studies of alliance reliability and helps to explain why some alliances are stabilizing while others are associated with crises and war. The nonlinear consequences of Protégé's commitment seem to us to constitute another "paradox of war."