Indirect reciprocity in three types of social dilemmas

Author-Highlights•We examine stability of indirect reciprocity in general simultaneous-move games.•We study Snowdrift (SG), Stag Hunt (SH), and Prisoner׳s Dilemma (PD) games.•Strong punishment via bad reputations for defectors is only necessary in SG and PD.•Punishment for unconditional cooperators stabilizes reciprocation in all the three games.•Social norms that unfairly favor reciprocators enhance cooperation in SH.

Indirect reciprocity is a key mechanism for the evolution of human cooperation. Previous studies explored indirect reciprocity in the so-called donation game, a special class of Prisoner׳s Dilemma (PD) with unilateral decision making. A more general class of social dilemmas includes Snowdrift (SG), Stag Hunt (SH), and PD games, where two players perform actions simultaneously. In these simultaneous-move games, moral assessments need to be more complex; for example, how should we evaluate defection against an ill-reputed, but now cooperative, player? We examined indirect reciprocity in the three social dilemmas and identified twelve successful social norms for moral assessments. These successful norms have different principles in different dilemmas for suppressing cheaters. To suppress defectors, any defection against good players is prohibited in SG and PD, whereas defection against good players may be allowed in SH. To suppress unconditional cooperators, who help anyone and thereby indirectly contribute to jeopardizing indirect reciprocity, we found two mechanisms: indiscrimination between actions toward bad players (feasible in SG and PD) or punishment for cooperation with bad players (effective in any social dilemma). Moreover, we discovered that social norms that unfairly favor reciprocators enhance robustness of cooperation in SH, whereby reciprocators never lose their good reputation.