A Necessary and Sufficient Condition for Peace∗

This paper examines the possibility for two contestants to agree on a peace settlement thereby avoiding a contest, in which each would exert a costly effort given the posterior distributions inferred from the negotiation. I find a necessary and sufficient condition of the prior distributions for there to exist a negotiation mechanism that admits a peace-ensuring perfect Bayesian equilibrium. The finding is based on an analysis of two-player all-pay contests that unifies the methods previously separated by the difference in discrete versus continuous distributions, and handles continuation plays that may cause empty best responses and infinitesimal effort costs for all but one type of a contestant who deviated previously. When a contestant becomes ex ante stronger, the peace condition is more likely to hold, though the strengthened contestant need not gain in the peace payoff, nor does the opponent need to exert more efforts to punish the former should the former deviate. The peace condition is also robust to equilibrium refinements such as the intuitive criterion and universal divinity. ∗The financial support from the Social Science and Humanities Research Council of Canada is gratefully acknowledged. I thank Beth Allen, Mariagiovanna Baccara, Fredrik Ødegaard, Scott Page, Mike Peters, John Quah, Roberto Serranos, Hanzhe Zhang and seminar participants of the 2016 NSF/NBER/CEME Mathematical Economics Conference at Johns Hopkins University, 2017 NSF/CEME Decentralization Conference at the University of Michigan, 2017 Canadian Economic Theory Conference at the University of British Columbia, the Michigan State University, the Lingnan University College of Sun YatSen University, and the Ivey School of Business at the University of Western Ontario for their comments. †Department of Economics, University of Western Ontario, London, Ontario, [email protected], http://economics.uwo.ca/faculty/zheng/.