The prisoners' dilemma, congestion games and correlation

Social dilemmas, in particular the prisoners' dilemma, are represented as congestion games, and within this framework soft correlated equilibria as introduced by Forgó F. (2010, A generalization of correlated equilibrium: A new protocol. Mathematical Social Sciences 60:186-190) is used to improve inferior Nash payoffs that are characteristic of social dilemmas. These games can be extended to several players in different ways preserving some important characteristics of the original 2-person game. In one of the most frequently studied models of the n-person prisoners' dilemma game we measure the performance of the soft correlated equilibrium by the mediation and enforcement values. For general prisoners' dilemma games the mediation value is ∞, the enforcement value is 2. This also holds for the class of separable prisoners’ dilemma games.

A generalization of correlated equilibrium: A new protocol

A new correlation scheme (leading to a special equilibrium called “soft” correlated equilibrium) is introduced for finite games. After randomization over the outcome space, players have the choice either to follow the recommendation of an umpire blindly or freely choose some other action except the one suggested. This scheme can lead to Pareto-better outcomes than the simple extension introduced by [Moulin, H., Vial, J.-P., 1978. Strategically zero-sum games: the class of games whose completely mixed equilibria cannot be improved upon. International Journal of Game Theory 7, 201–221]. The informational and interpretational aspects of soft correlated equilibria are also discussed in detail. The power of the generalization is illustrated in the prisoners’s dilemma and a congestion game.