In broad daylight: Full information and higher-order punishment opportunities promote cooperation

The expectation that non-cooperators will be punished can help to sustain cooperation, but there are competing claims about whether opportunities to engage in higher-order punishment (punishing punishment or failure to punish) help or undermine cooperation in social dilemmas. In a set of experimental treatments, we find that availability of higher-order punishment increases cooperation and efficiency when subjects have full information on the pattern of punishing, including its past history, and opportunities to punish are unrestricted. Availability of higher-order punishment reduces cooperation and efficiency if it is restricted to counter-punishing alone, if past history is unavailable, and if there is a dedicated counter-punishment stage.