Survey of Indirect Reciprocity

Hannelore Brandt, Hisashi Ohtsuki, Yoh Iwasa, and Karl Sigmund

Summary. This survey deals with indirect reciprocity, i.e. with the possibility that altruistic acts are returned, not by the recipient, but by a third party. After briefly sketching how this question is dealt with in classical game theory, we turn to models from evolutionary game theory. We describe recent work on the assessment of interactions, and the evolutionary stability of strategies for indirect reciprocation. All stable strategies (the 'leading eight') distinguish between justified and non-justified defections, and therefore are based on non-costly punishment. Next we consider the replicator dynamics of populations consisting of defectors, discriminators and undiscriminating altruists. We stress that errors can destabilise cooperation for strategies not distinguishing justified from unjustified defections, but that a fixed number of rounds, or the assumption of an individual's social network growing with age, can lead to cooperation based on a stable mixture of undiscriminating altruists and of discriminators who do not distinguish between justified and unjustified defection. We describe previous work using agent-based simulations for 'binary score' and 'full score' models. Finally, we survey the recent results on experiments with the indirect reciprocation game.

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