Speed of retaliation and international cooperation

Abstract

Many international interactions are structured like a prisoner’s dilemma because there are incentives to cooperate but also incentives to defect. In an infinitely repeated prisoner dilemma interaction, valuing the future highly enough by discounting the future less can ensure cooperation. Another factor that affects international cooperation in an infinitely repeated prisoner’s dilemma interaction is how quickly actors can respond to defection with retaliation, in other words, the speed of retaliation. Speeding up retaliation to ensure cooperation is an attractive strategy because it is flexible. It can be adapted to the particular characteristics of a dyad of cooperation and can vary with different actors and even different forms of cooperation between the same two actors. An analysis of an infinitely repeated prisoner’s dilemma interaction shows that if speeding up retaliation is costless, payoffs are constant in time, and the temptation payoff is reduced in proportion to the speed-up of retaliation, then no matter how unfavorable the starting discount factor and unfavorable the payoffs, speeding up retaliation can make cooperation sustainable. This, in combination with its inherent flexibility, makes speeding up retaliation a potentially powerful tool to make cooperation sustainable. Because speeding up retaliation likely has some implementation costs and because prisoner dilemma payoffs may not be constant/even in time, there are limits on when speeding up retaliation is effective. However, the analysis shows that if implementation costs are not too high, payoffs are not too uneven, or, if uneven in a particularly unfavorable way, punishment, when inflicted, is sufficiently punishing, then speeding up retaliation can still be effective in ensuring sustained cooperation.