Long-term Competition in a Dynamic Game: The Cold Fish War

This article presents a model of credible, voluntary, collective agreements in a dynamic game. These agreements are implicit in collections of history-dependent (threat) strategies. I consider the strategies in a game of resource exploitation. Credibility is represented by perfect equilibrium. Voluntarism requires at least that all behavior be supported by the threat of collapse of the agreement, which would return the players to the memoryless equilibrium. Collective rationality requires that the agreement be robust to the possibility of mutually beneficial renegotiation. I analyze the set of agreements meeting each of these restrictions.