The paradoxes of revenge in conflicts

We consider a differential game of a conflict between two factions who both have a desire to exact revenge. We show that, in contrast to conventional wisdom, the desire for revenge need not lead to escalation of conflicts. Surprisingly, in the open-loop equilibrium, the weaker faction exerts a higher effort when the stronger faction's military capability increases. This result is not possible in the absence of a desire for revenge. The closed-loop equilibrium is characterized by a self-deterrence effect: Anticipating the future retaliation of the opponent, a faction has an incentive to exert lower effort today. This strengthens the tendency to a stable steady state and paradoxically may decrease the factions' effort below the levels exerted in the case without revenge. We discuss some applications of our results and also offer an explanation of a puzzling empirical result obtained by Jaeger and Paserman (2007) in their study of the Israeli-Palestinian conflict. We also discuss the implications of revenge-dependent preferences for welfare economics and their strategic value as commitment devices.