Cooperation Over Finite Horizons : A Theory and Experiments

This paper proposes a theory of cooperation over finite horizons, focusing on public good contribution games, that implies the broadly documented feature of decreasing cooperation over time. The central assumption is that there are two types of players: those who only care about their own material payoffs, and those who reciprocate others' contributions. The main result is that if reciprocity functions satisfy some regularity conditions, then generically there is a unique perfect equilibrium, in which contributions are decreasing. In this equilibrium, selfish players contribute to induce subsequent contributions by reciprocal players, and this incentive diminishes as the end of the play approaches. The model explains the puzzling restart effect and is consistent with various other empirical findings. In one-shot games, the model predicts no contributions.We also report the results of a series of experiments, using a probabilistic continuation design in which after each round, the game is restarted with low probability. The results support the implications of our model that the restart effect is present even with experienced players, whereas, in one-shot games, contributions disappear with experience. We show that experienced players correctly foresee the pattern of contributions, suggesting that the declining pattern comes from equilibrium play. We also identify the presence of conditional reciprocity among experienced players, and document that selfish players (identified exogenously) stop contributing earlier than reciprocal players, as implied by the model