Social Dilemma and Emergence of Cooperation

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This research studies prisoner's dilemma and social dilemma from the standpoint of von Neumann-Morgenstern stable sets with farsightedness of players. The following are the main results.1 Prisoner's dilemma: When two players behave independently, the unique stable set consists of two states: both cooperate or both defect. If mixed strategies are allowed, every pair of mixed strategies is included in a stable set. When they are allowed to communicate, even though agreements are not binding, there exists a unique stable set consisting of one outcome : both cooperate. If players use mixed strategies, all stable sets consist of Pareto optimal outcomes. Moreover, stationary equlibria in an alternating-move prisoner's dilemma game provide us with similar outcomes as stable sets.2 Social dilemma: In a social dilemma (a prisoner's dilemma with many players), even though no agreement among players is binding, outcomes in any stables set are Pareto optimal and individually rational.