Deterrence of a challenger by a defender is modeled by explicitly relating uncertainty and the credibility of retaliatory threats to the stability of an asymmetric deterrence relationship. In the two-person game model, each player either prefers to fight rather than back down or prefers the reverse. A player knows its own preference, but is uncertain of its adversary's. The challenger may choose to accept the status quo or initiate a crisis; in the latter case, the defender may capitulate or defend; if it defends, the challenger must either back down or face a situation of open conflict. The perfect Bayesian equilibria of the game are determined, interpreted, and illustrated with historical examples of the success or failure of deterrence.
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Zagare et al. (1993) studied this question.