Figure 4: Two behavioural experiments are consistent with model predictions.

(a) In Experiment 1, subjects play an optional public goods game followed by a compulsory public goods game. The average fraction contributed in the compulsory game is significantly lower among subjects who opt out of the optional game (Rank-sum, N=73, P=0.006). Thus, as predicted, loners contribute less in compulsory games. (b) In Experiment 2, subjects play an optional game followed by a compulsory game with costly punishment. Subjects indicate how much (0, 1 or 2) they would punish each possible contribution level in the compulsory game. Subjects who opt out of the optional game invest significantly more in punishing those that contribute the maximal amount (Rank-sum, N=196, P=0.003). Thus as predicted, loners engage in more antisocial punishment. All games are one-shot interactions among four players, with contributions to the public good multiplied by 2. Punishment technology is 3:1. Results are robust to various controls and alternate methods of analysis; Supplementary Note.