Subgame-Perfection in Stochastic Games with Perfect Information and Recursive Payoffs

We present a model of adaptive economic agents that are k periods forward looking. Agents in our model are randomly matched to interact in finitely repeated games. They form beliefs by relying on their past experience in the same situation (after the same recent history) and then best respond to these beliefs looking k periods ahead. We establish almost sure convergence of our stochastic process and characterize absorbing sets. These can be very different from the predictions in both the fully rational model and the adaptive, but myopic case. In particular we find that also Non-Nash outcomes can be sustained almost all the time whenever they are individually rational and satisfy an efficiency condition. We then characterize stochastically stable states in 22 games and show that under certain conditions the efficient action in Prisoner’s Dilemma games and Coordination games can be singled out as uniquely stochastically stable. We show that our results are consistent with typical patterns observed in experiments on finitely repeated Prisoner’s Dilemma games. Finally, if populations are composed of some myopic and some forward looking agents parameter constellations exists such that either might obtain higher average payoffs.