December 2019
It is common for researchers studying infinite horizon dynamic games in a lab experiment to pay participants for a randomly chosen round or all rounds. We argue that these payment schemes typically implement different outcomes than the target game for a large class of solution concepts (e.g., subgame perfect equilibria, Markov equilibria, renegotiation-proof equilibria, rationalizability). For instance, a compensation scheme that pays subjects for a randomly chosen round induces a time-dependent discounting function. Future periods are discounted more heavily than the discount rate in a way that can change the theoretical predictions both quantitatively and qualitatively. We rigorously characterize the mechanics of the problems induced by these payment methods, developing measures to describe the extent and shape of the distortions. We also establish that a simple payment scheme, paying participants for the last (randomly occurring) round, robustly implements the predicted outcomes for any infinite horizon dynamic game with time separable utility, exponential discounting and a payoff invariant solution concept.