Fig. 3.

Does a larger behavioral repertoire make cooperation easier to evolve? We evolved a well-mixed population of $N=100$ haploid, asexual individuals reproducing according to the copying process (49) with an individual’s fitness determined by playing pairwise iterated public goods games with selection strength $\sigma =10$, with each game played for 1,000 rounds. We calculated ensemble mean fitness across ${10}^5$ replicate populations, each evolved under weak mutation for at least ${10}^6$ fixation events. We compared populations with only two investment choices available, $C_1=0$ and $C_2=1$, versus populations in which players could choose among 11 levels of investment, between 0 and 1 in increments of 0.1. In both cases evolution occurred on the full set of memory-1 strategies. When the ratio of public benefit to individual cost is small, two-choice populations evolve to low mean fitness and exhibit little cooperation; whereas, 11-choice populations evolve higher fitness and higher levels of investment in the public good. However, when the ratio of public benefit to individual cost is higher two-choice populations evolve strategies that maximize the public good, whereas 11-choice populations are less cooperative and receive roughly 10% payoff reduction compared with the two-choice case. Thus, a larger repertoire of behavioral options can either facilitate or impede the evolution of cooperation, depending upon the public return on individual investment.