Figure 1

A hypothetical threshold public goods game involving a prehistoric hunt (for modern examples, see^21,22). A minimum number of hunters (\(\tau = 5\)) must cooperate to successfully surround and kill an animal or their efforts are wasted. A cooperator’s payoff is W if the threshold is met and X if it is not (blue line). All members share the meat (\(n=8\)); therefore, the highest payoff goes to defectors (red line) regardless of whether the hunt is successful (payoff Y) or not (payoff Z). However, if an individual is likely to be the pivotal hunter, i.e., the hunter that brings the group above the threshold for a successful hunt, then it is incentivised to cooperate because the payoff to a defector when the threshold is not met is less than the payoff to a cooperator when the threshold is met (\(Z < W\)).