Revenge or continued attack and defense in defender–attacker conflicts

Existing literature has demonstrated that exacting revenge can have a self-deterrence effect and a value of revenge effect. The former means that each player will decrease effort when competing for a resource because of fear of a rival’s revenge while the latter implies that each player will increase effort in the revenge period. Moreover, the self-deterrence effect could outweigh the value of revenge effect, implying that revenge could be helpful in stabilizing conflicts, a phenomenon known as the paradox of revenge. We re-examine the two effects and the paradox of revenge in defender–attacker conflicts, considering a scenario in which a defender (and only the defender) who was attacked in the first period takes revenge on the attacker in the subsequent period. We demonstrate that whether or not these results hold, depends on how much the defender values revenge and the difference between the two players’ efficiencies of effort. More interestingly, we show that a sufficiently large revenge value for the defender can deter an attack from the attacker in the first place.