A Revision-Game Concept of Stability and Cooperation in Games

From conjectural-variation equilibrium to Riley equilibrium to stable sets and other notions of far-sighted stability, economic theorists have considered various solution concepts in games that take in to account the possibility that players may react to deviations by other players. This paper proposes a revision-games approach to study this problem: players can adjust their actions and react to other players’ adjustments until all players settle on some action profile or, with vanishing probability, the action profile is exogenously frozen. The resulting solution concept is well-defined for all n-player normal-form games and is always nonempty in finite games. It pins down the efficient action profile in coordination games and predicts a unique outcome in the prisoners’ dilemma, which entails a positive amount of cooperation. We discuss predictions in Bertrand competition, matching pennies, and applications to various other games, and explain why three features of our concept (asynchronicity, settlement rule, and Markov refinement), when combined, play a key role to capture collaboration.