Zero-Sum Revision Games

Abstract

In a zero-sum asynchronous revision game, players can revise their actions only at exogenous random times. Players’ revision times follow Poisson processes, independent across players. Payoffs are obtained only at the deadline by implementing the last prepared actions in the ‘component game’. The value of this game is called revision value. We characterize it as the unique solution of an ordinary differential equation and show it is continuous in all parameters of the model. We show that, as the duration of the game increases, the limit revision value does not depend on the initial position and is included between the min-max and max-min of the component game. We fully characterize the equilibrium in 2?2 games. When the component game minmax and maxmin differ, the revision game equilibrium paths have a wait-and-wrestle structure: far form the deadline, players stay put at sur-place action profile, close to the deadline, they take best responses to the action of the opponent.