The Desire for Revenge and the Dynamics of Conflicts

We model an infinitely-repeated conflict between two factions who both have a desire to exact revenge for past destruction suffered. The destruction suffered by a player is a stock that grows according to his opponent’s destructive efforts and the rate at which past destruction is forgotten (i.e., depreciates). This gives a differential game. We find that a desire for revenge can cause a low-ability player to exert a higher effort than a high-ability player, which means that the former may have a higher probability of success in a given period. Given a desire for revenge, we find that, the conflict initially escalates and eventually reaches a steady state. When there is no desire for revenge, the conflict reaches a steady state immediately. The conflict is sufficiently less destructive if the rate at which past destruction is forgotten is sufficiently high. We briefly discuss how our results apply to the USA’s invasion of Iraq, reconstruction assistance to Lebanon after the 1975-1990 war, and the Israeli-Palestinian conflict.