Quantitative determination of the level of cooperation in the presence of punishment in three public good experiments

Strong reciprocity is a fundamental human characteristic associated with our extraordinary sociality and cooperation. Laboratory experiments on social dilemma games and many field studies have quantified well-defined levels of cooperation and propensity to punish/reward. The level of cooperation is observed to be strongly dependent on the availability of punishments and/or rewards. Here, we propose an operational approach based on the evolutionary selection of prosocial behaviors to explain the quantitative level of the propensity to punish in three experimental set-ups. A simple cost/benefit analysis at the level of a single agent, who anticipates the action of her fellows, determines an optimal level of altruistic punishment, which explains quantitatively experimental results on a third-party punishment game, the ultimatum game and an altruistic punishment game. We also report numerical simulations of an evolutionary agent-based model of repeated agent interactions with feedback by punishments, which confirms that the propensity to punish is a robust emergent property selected by the evolutionary rules of the model. The cost-benefit reasoning is not to be taken literally but rather to embody the result of the selection pressure of co-evolving agents that have make them converge to their preferences (which can be seen as either hard-wired and/or culturally selected). In this view, the prosocial preference of humans is a collective emergent process, robustly selected by adaptation and selection. Our main contribution is to use evolutionary feedback selection to quantify the value of the prosocial propensity to punish, and test this prediction on three different experimental set-ups.