Person:

Rand, David Gertler

The standard model for direct reciprocity is the repeated Prisoner's Dilemma, where in each round players choose between cooperation and defection. Here we extend the standard framework to include costly punishment. Now players have a choice between cooperation, defection and costly punishment. We study the set of all reactive strategies, where the behavior depends on what the other player has done in the previous round. We find all cooperative strategies that are Nash equilibria. If the cost of cooperation is greater than the cost of punishment, then the only cooperative Nash equilibrium is generous-tit-for-tat (GTFT), which does not use costly punishment. If the cost of cooperation is less than the cost of punishment, then there are infinitely many cooperative Nash equilibria and the response to defection can include costly punishment. We also perform computer simulations of evolutionary dynamics in populations of finite size. These simulations show that in the context of direct reciprocity, (i) natural selection prefers generous tit-for-tat over strategies that use costly punishment, and (ii) that costly punishment does not promote the evolution of cooperation. We find quantitative agreement between our simulation results and data from experimental observations.

We examine cooperation in repeated interactions where intended actions are implemented with noise but intentions are perfectly observable. Observable intentions lead to more cooperation compared to control games where intentions are unobserved, allowing subjects to reach similar cooperation levels as in games without noise. Most subjects condition exclusively on intentions, and use simpler, lower-memory strategies compared to games where intentions are unobservable. When the returns to cooperation are high, some subjects are tolerant, using good outcomes to forgive attempted defections; when the returns to cooperation are low, some subjects are punitive, using bad outcomes to punish accidental defections.