Integrative experiments identify how punishment affects welfare in public goods games

Despite decades of research, the conditions under which punishment promotes cooperation remain unclear. Through an integrative experiment varying 14 design parameters of public goods games across 360 experimental conditions (147,618 decisions from 7100 participants), we reveal substantial heterogeneity in punishment effectiveness: Its impact on welfare ranges from 43% improvement to 44% reduction depending on the game parameters. To characterize these patterns, we developed models that outperformed human forecasters in predicting punishment effectiveness in new experiments. Communication emerges as the most important factor, followed by contribution framing (opt out versus opt in), contribution type (variable versus all-or-nothing), game length, and outcome visibility, though these factors often interact. The results reframe the debate from whether punishment works to when it does, demonstrating how integrative experiments enable discovery of generalizable patterns in social phenomena.