We use response curves in a repeated game to analyze key aspects of mutual deterrence: escalation, de-escalation, incomplete deterrence, and deterrence by denial. In this approach, episodes of violence are due to interacting response curves, which disincentivize opponents from attacking through...

We prove the existence of a trembling-hand perfect equilibrium within a class of compact, metric, and possibly discontinuous games. Our conditions for existence are easily verified in a variety of economic games.

We obtain conditions on the primitives of a Bayesian game with infinitely many types and/or strategies that ensure the existence of a perfect Bayes-Nash equilibrium. The main existence results are illustrated in the context of all-pay auctions.