Uncertainty and the role of the pawn in extended deterrence

This paper develops an incomplete information model of extended deterrence relationships. It postulates players who are fully informed about the costs of war and all other relevant variables, save for the values their opponents place on the issues at stake, i.e., the pawn. We provide consistent and intuitively satisfying parallel definitions for two types of players, Hard and Soft, in terms of the parameters of our model. We also answer several particular questions about the strategy choices of players in an extended deterrence relationship and, by identifying all the Perfect Bayesian Equilibria of the game model we construct, specify typical behavior patterns.Our most general finding is that an Extended Deterrence Game always has a unique Perfect Bayesian Equilibrium with a rather simple form. A challenger initiates for certain if the pawn is valuable enough to it and never challenges otherwise, Likewise, a defender always resists if the pawn is valuable enough and never resists otherwise.In addition to identifying threshold values for optimal strategic choice, we provide existence conditions for the two distinct types of Perfect Bayesian Equilibria. This permits us to identify the exact set of conditions associated with bluffing strategies and to develop a theory of the necessary and sufficient conditions for extended deterrence crisis initiation and its resolution.