The evolution of conformity in the repeated PGG.

Abstract

<p>Repeated PGG with <i>n</i> = 10, <i>m</i> = 4 and <i>r</i> = 1.6. <b>(a)</b> Phase portrait of the adaptive dynamics Eq (4). Stable equilibria and unstable equilibria are marked by solid dots and empty dots, respectively.<i>p</i>^* = 1/3 (the blue dash line). A trajectory of Eq (4) starting from (<i>x</i>, <i>p</i>) converges to the stable cooperative equilibrium (1, <i>p</i>) if <i>p</i> > <i>p</i>^*, and converges to the unstable defective equilibrium (0, <i>p</i>) if <i>p</i> < <i>p</i>^*. <b>(b)</b> Monte-Carlo simulation result for a population of size 100. At the beginning of each time step, individuals are randomly divided into 25 groups and play the repeated PGG. In each time step, an average of 10 individuals are chosen to update, where they imitate actions that perform better with a probability proportional to the payoffs obtained in the repeated PGG. With probability 0.1, one of the 100 individuals is chosen to adopt a new strategy (i.e., the average individual mutation rate is 0.001) by adding a small random value (draw from Gaussian noise (0, 0.1)) on its former strategy. Monte-Carlo simulation also shows that conditional altruistic strategies (i.e., <i>x</i> = 1 with large <i>p</i>) and unconditional selfish strategies (i.e., <i>x</i> = 1 with small <i>p</i>) are bistable, and the population oscillates between <i>x</i> = 1 and <i>x</i> = 0.</p