Strong reciprocity refers to the willingness to sacrifice one's own material selfinterest to punish others for opportunistic actions. This propensity provides a decentralized mechanism for the enforcement of social norms, but its extent and persistence poses a theoretical puzzle. Since opportunistic individuals choose optimally to comply with or violate norms based on the likelihood and severity of sanctioning they anticipate, such individuals will always outperform reciprocators within any group. The presence of reciprocators in a group can, however, alter the behavior of opportunists in such a manner as to benefit all members of the group (including reciprocators). We show that under these circumstances, reciprocators can invade a population of opportunists when groups dissolve and are formed anew according to a process of purely random (non-assortative) matching. Furthermore, even when these conditions are not satisfied (so that an opportunistic population is stable) there may exist additional stable population states in which reciprocators are present
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