Published online by Cambridge University Press: 12 November 2014
This article introduces a model of war and peace in which leaders believethat their adversaries might be crazy types who always behave aggressively,regardless of whether it is strategically optimal to do so. In the model,two countries are involved in a dispute that can either end in a peacefulsettlement or escalate into ‘limited war’ or ‘total war.’ If it is commonknowledge that the leaders of the countries are strategically rational, thenthe only equilibrium outcome of the model is peace. Yet if a leader believesthat there is a chance that her adversary is a crazy type, then even astrategically rational adversary may have an incentive to adopt a madmanstrategy in which he pretends to be crazy. This leads to limited war withpositive probability, even when both leaders are strategically rational. Thearticle shows that despite having two-sided incomplete information, themodel has a generically unique equilibrium. Moreover, the model identifiestwo countervailing forces that drive equilibrium behavior: a reputationmotive and a defense motive. When the prior probability that a leader iscrazy decreases, the reputation motive promotes less aggressive behavior bythat leader, while the defense motive pushes for more aggressive behavior.These two forces underlay several comparative statics results. For example,the study analyzes the effect of increasing the prior probability that aleader is crazy, and the effect of changing the relative military strengthsof the countries, on the equilibrium behavior of both leaders. The analysisalso characterizes the conditions under which the madman strategy isprofitable (or not), which contributes to the debate in the literature aboutits effectiveness.
Avidit Acharya is Assistant Professor of Political Science, StanfordUniversity, Encina Hall West, Room 406, Stanford, CA 94305-6044 USA(email: avidit@stanford.edu).Edoardo Grillo is Unicredit and Universities Foscolo Fellow, CollegioCarlo Alberto, Via Real Collegio, 30, 10024 Moncalieri (Torino), Italy(email: edoardo.grillo@carloalberto.org). We are grateful toRoland Bénabou, James Fearon, Mark Fey, Adam Meirowitz, JohnLondregan, Juan Ortner, Satoru Takahashi, the editor, two anonymousreferees, and especially Stephen Morris and Kristopher Ramsay, forvaluable comments and discussions. We also thank audiences atVanderbilt, Princeton and the University of Rochester for theircomments. We are responsible for any remaining errors.