Constructing Strategies in the Indefinitely Repeated Prisoner's Dilemma Game

Abstract

We propose a new approach for running lab experiments on indefinitely repeated games with high continuation probability. This approach has two main advantages. First, it allows us to run multiple long repeated games per session. Second, it allows us to incorporate the strategy method with minimal restrictions on the set of pure strategies that can be implemented. This gives us insight into what happens in long repeated games and into the types of strategies that subjects construct. We report results obtained from the indefinitely repeated prisoner's dilemma with a continuation probability of δ =0.95. We find that during such long repeated prisoner's dilemma games, cooperation drops from the first period of a supergame to the last period of a supergame. When analyzing strategies, we find that subjects rely on strategies similar to those found in the literature on shorter repeated games --- specifically Tit-For-Tat, Grim Trigger, and Always Defect. However, we also identify features of strategies that depend on more than just the previous period that are responsible for the drop in cooperation within supergames, but that may be overlooked when using the common strategy frequency estimation approach.

Keywords: Indefinitely Repeated Games, Prisoners' Dilemma, Experiments, Cooperation, Experimental Design, Strategies