Risk and Repeated Games : Is Random Termination a Reasonable Proxy For Discounting?

This paper looks to see if departures from risk neutrality cause subjects to behave differently in randomly terminated supergames compared to infinitely discounted supergames. I show that if subjects have a strictly monotonic utility function, and that utility function is applied to their entire income stream instead of their period by period earnings, then the critical discount factor, δ ∗ , needed to support cooperation in the repeated Prisoner's Dilemma differs between discounted and randomly terminated supergames as subjects become more risk averse/seeking. I then take this theoretical result into the lab where I have subjects play randomly terminated supergames and supergames featuring discounted payoffs over an "infinite" time horizon using a unique experimental design. This design allows subjects to opt out of continuing to play the discounted supergames and instead receive a continuation payoff as compensation for every period of the supergame they choose not to play. The lab results show that there is no statistically significant difference between what actions subjects chose to play in randomly terminated supergames and those they chose to play in discounted supergames, even when their risk attitude is controlled for. Simple, two period patterns of stage game outcomes are more likely to emerge in discounted supergames than they are in randomly terminated supergames