Horizon and Cooperation: How the Length of a Game Affects Player Cooperation.

Abstract

The study of conflict and cooperation in competitive situations has contributed greatly to various fields. From modelling to describing behaviour, the application of game theory in these fields has significantly improved their depth and robustness. Despite the field’s usefulness there is still a significant disconnect between theoretical predictions and what is evidenced empirically. Illuminating this gap greatly explains the motivation behind this empirical study. An experiment of unique parameters is conducted in order to test the robustness of the contemporary literature and explore how cooperation evolves with horizon. The study finds that cooperation does not always behave as the conventional literature suggests, even when multiple repetitions allow for subjects to gain experience. Game theoretic literature has found that in finitely repeated games the evolution of cooperation follows a distinct pattern of early cooperation followed by defection near the end of the game (Embrey et al. 2016). However our results show that this pattern does not always hold. We find that in a “stranger” setting, where players are paired only for a single round of play before being re-matched with another, they will disregard the horizon of finitely repeated PD games and treat the supergame as a series of one shot games. This finding was robust even when experience was accounted for. Consistent with recent literature on infinitely repeated games, horizon and experience both have a significant effect on cooperation, with the latter magnifying the former. However contrary to other studies on the subject, we observe that increases in the horizon decreased cooperation. This study suggests that parameters play an important role in how key variables affect cooperation and that they need to be factored in when using the prisoner’s dilemma.