Deterrence in Contests

This paper explores the role of deterrence in contests. As a general rule, we show that for a deterrence strategy to be played by rational agents, it is necessary that the contest be destructive. We show for a very general class of functions that pure strategy deterrence equilibria where contestants deter one another do not exist. A corollary of this finding is that under fairly general conditions, agents should always be expected to engage in contests. Applied to international relations, our results imply that war is always a potential outcome despite deterrence attempts.