Figure 3: The impact of group size and memory capacity on cooperation.
We calculated the relative volumes of robust cooperation – that is, the absolute volume of robust cooperative strategies divided by the total volume of robust cooperators and defectors – and compared this to the relative volume of defectors (solid lines) by numerically integrating Eqs. 2, 3. We also verified these analytic results by randomly drawing 106 cooperative and 106 defecting strategies and determining their success at resisting invasion from 105 random mutants with the same memory (points). We calculated player’s payoffs by simulating 2 × 103 rounds of a public-goods game. We then plotted the relative volumes of robust cooperators and robust defectors as a function of group size n (with fixed memory m = 1, left) and as a function of memory capacity m (with fixed group size n = 2, right). Increasing group size increases the relative volume of robust defection; while increasing memory length increases the relative volume of robust cooperation. In all calculations and simulations we used cost C = 1 and benefit B as indicated in the figure.
