Figure 3

The effects of a reward w_i and the game size N on the internal equilibrium x*.

We assume the numbers of players between species to be equal, i.e., d₁ = d₂ = d. Thus, the game size for each species is defined by N and N = d + 1. (a) Given a relatively low reward intensity (i.e., w = 0.8), the internal equilibrium x* is above 0.5 in small groups (e.g., N = 2 or N = 3). (b) For pairwise games, the equilibrium is always above 0.5 for any reward intensity. (c) When the size of the mutualistic group is large (i.e., N = 8), the internal equilibrium can shift from a small value (below 0.5) to a large value (above 0.5) with a rise in the collective reward. The other parameters are fixed at b_i = 2, c_i = 1 and M_i = 1.