Coordinated and uncoordinated punishment in a team investment game

Coordinated punishment occurs when punishment requires a specific number of punishers to be effective, otherwise, no damage will be inflicted on the target. While societies often rely on this punishment device, its benefits are unclear compared to uncoordinated punishment, where punishment decisions are substitutes. In this paper, we compare the efficacy of coordinated and uncoordinated punishment in a team investment game with two investors and one allocator. Our findings indicate that coordinated punishment results in higher levels of cooperation and reciprocity, as measured by the levels of joint investment and the return by allocators. Importantly, this does not translate into higher payoffs: investors use punishment more frequently when this is coordinated, which destroys the efficiency gains generated by the highest investment. In fact, our results suggest that the highest level of efficiency would be achieved if investors were not allowed to punish.