Defectors’ intolerance of others promotes cooperation in the repeated public goods game with opting out

Theoretical and experimental work on opting out (conditional dissociation) in social dilemmas has largely focused on opting out against defectors to raise cooperation. Analyzing stable Nash equilibria (NE) of a repeated multi-player public goods game (PGG) with opting out, this paper shows that other opting-out mechanisms can more effectively promote cooperation. The strongest promotion of cooperation occurs when only homogeneous groups (all cooperators or all defectors) voluntarily stay together between rounds for sufficiently many rounds. This outcome emerges if defectors are completely intolerant of cooperators and opt out whenever a cooperator is present, causing all heterogeneous groups to disband after one round. By simplifying strategies so each individual is fixed as a Cooperator or Defector for the entire game and has an opting-out rule based on the number of cooperators in the group, we derive fitnesses via expected per-round payoffs at equilibrium group distributions and identify conditions under which coexistence equilibria and elevated cooperation arise.

Vlastimil Křivan, Ross Cressman