Group size effects and critical mass in public goods games.

Understanding whether the size of the interacting group has an effect on cooperative behavior has been a major topic of debate since the seminal works on cooperation in the 1960s. Half a century later, scholars have yet to reach a consensus, with some arguing that cooperation is harder in larger groups, while others that cooperation is easier in larger groups, and yet others that cooperation attains its maximum in intermediate size groups. Here we add to this field of work by reporting a two-treatment empirical study where subjects play a Public Goods Game with a Critical Mass, such that the return for full cooperation increases linearly for early contributions and then stabilizes after a critical mass is reached (the two treatments differ only on the critical mass). We choose this game for two reasons: it has been argued that it approximates real-life social dilemmas; previous work suggests that, in this case, group size might have an inverted-U effect on cooperation, where the pick of cooperation is reached around the critical mass. Our main innovation with respect to previous experiments is that we implement a within-subject design, such that the same subject plays in groups of different size (from 5 to 40 subjects). Groups are formed at random at every round and there is no feedback. This allows us to explore if and how subjects change their choice as a function of the size of the group. We report three main results, which partially contrast what has been suggested by previous work: in our setting (i) the critical mass has no effect on cooperation; (ii) group size has a positive effect on cooperation; (iii) the most chosen option (played by about 50% of the subjects) is All Defection, followed by All Cooperation (about 10% of the subjects), whereas the rest have a slight trend to switch preferentially from defection to cooperation as the group size increases.