Necessary and sufficient conditions for peace: Implementability versus security
This paper investigates the conditions for full preemption of conflicts in the form of all-pay auctions. I define two notions of conflict preemption: to implement peace on path with commonly expected continuation plays should one veto a peace proposal, or to secure that each player accepts a peace proposal no matter what continuation play he might expect to occur should he veto it. For each notion I prove a necessary and sufficient condition in terms of the primitives. The conditions imply that peace cannot be secured when the infimum of a player's type support is sufficiently low, regardless of the distribution functions of the players' types. The conditions also imply that peace can be implemented even when each player forecasts that should he veto peace the cost he incurs in the ensuing conflict is infinitesimal. The findings are obtained through a distributional method on two-player all-pay auctions that unifies the methods previously separated by discrete versus continuous distributions.