Coordination, Conflict, and Convention

A game-theoretic analysis of convention is developed that is sufficiently general to characterize conventions of justice where agents’ interest can diverge, especially conventions of conflictual coordination. Conventions can be arbitrary with respect to each other in either an indifference sense or a discretionary sense, and only discretionary-sense arbitrariness is crucial for conventions of justice. Basic conventions are defined as strict correlated equilibria of games having multiple such equilibria. More general conventions that can have history-dependent strategies are defined as equilibria of a sequence of games or supergame having multiple such equilibria. A convention is incumbent in a community when the member agents involved have common knowledge that they follow this convention, rather than some alternative convention.