Do Small Players Undermine Cooperation in Asymmetric Games?

I study an indefinitely repeated game where players can differ in size and investigate the implications for cooperative-looking behavior. A common approach to modeling such behavior is to appeal to trigger strategies, where deviation from the desired level of cooperation triggers a punishment phase. An alternative approach arises if players condition their actions on a stock of social goodwill, which is developed when players collectively choose more cooperative actions than the one-shot Nash (Benchekroun and Long in J Econ Behav Organ 67(1):239–252, 2008). Using data from two-person experimental games, I analyze an empirical model that combines these two approaches. I find nuanced support for each approach. For the social goodwill model, there is statistically important support in symmetric games and for larger players in asymmetric games, but not for smaller players.