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The authors consider a differential game of a conflict between two factions who both have a desire to exact revenge. They 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.
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