[A public goods] game supports cooperative outcomes only if the group is small, the returns to cooperation are high, the behavior of each group member is known with a high degree of accuracy by all of the other group members, errors in execution are infrequent, and group members are very patient and interactions typically endure for many periods. The reason for the ineffectiveness of reciprocal altruism for groups with several members is simple. In groups of two, a free-rider cannot go undetected because a player’s payoff reveals the other player’s behavior. Equally important, when one member defects in order to punish a Defector, the punishment is uniquely targeted on the Defector. But, in groups larger than two, a player cannot infer who has defected from the knowledge of his own payoff. Moreover, a retaliatory defection punishes not only the initial defector, but also all other members of the group. Moreover, other group members may not have observed the initial defection and hence may think that a retaliatory defection is a free-riding defection, inviting further retaliatory defections.
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