Long Horizon Repeated Games: How Does Ending Rule Affect Decisions in High Δ Games

Abstract

This paper looks to see if subjects approach long, indefinitely repeated Prisoner's Dilemma games featuring discounted payoffs with an option to opt out differently from how they approach long, indefinitely repeated Prisoner's Dilemma games that are randomly terminated. I show under relatively general assumptions that the critical δ ∗ -value, above which cooperation can be supported as a Subgame Perfect Equilibrium, differs between the two environments. A between-subject design with δ = 0.98 was used to determine if subject behavior did vary by treatment. First period and all period cooperation rates were found to be higher in the random termination treatment compared to the discounted treatment. The evolution of cooperation across supergames also differed between the two treatments. Behavior in the discounted treatment did not follow the patterns typically observed in the literature. Lastly, the Strategy Frequency Estimation Method (SFEM) was used to determine whether or not subjects in different treatments used different repeated game strategies. I find that subjects in the discounted treatment were more likely to play strategies that defect initially (All D, STFT), but cooperative subjects tended to play more forgiving strategies (TFT, STFT). Conversely, subjects in the randomly terminated treatment tended to play more initially cooperative, yet less forgiving strategies (Grim, Grim2).