Equilibrium vengeance

The efficiency-enhancing role of the vengeance motive is illustrated in a simple social dilemma game in extensive form. Incorporating behavioral noise and observational noise in random interactions in large groups leads to seven continuous families of (short run) Perfect Bayesian equilibria (PBE) that involve both vengeful and non-vengeful types. A new long run evolutionary equilibrium concept, Evolutionary Perfect Bayesian Equilibrium (EPBE), shrinks the equilibrium set to two points. In one EPBE, only the non-vengeful type survives and there are no mutual gains. In the other EPBE, both types survive and reap mutual gains.