Figure 4
From: Evolution of cooperation and consistent personalities in public goods games
The time evolution of the system in assortative public goods games. (a)–(d) The frequency of different strategies as a function of time. Top panels show replicator dynamics solutions and the bottom panels result form the simulations in a population of \(N=5000\) individuals. The system shows two different periodic orbits. A cooperative periodic orbit, with higher level of cooperation for larger \(r_2\), \(r_2=4.8\) in (a), and a defective periodic orbit, for small \(r_2\), \(r_2=2.4\) in (b). In the fixed point of the dynamics for small \(r_2\) but larger than \(2-r_1/g\), as in (c) where \(r_2=2\), only \(C_1C_2\) cooperators evolve, and for large \(r_2\), \(r_2=5.6\) in (d), both \(C_1C_2\) and \(D_1C_2\) evolve. Here, \(g=10\), \(\nu =10^{-3}\), \(c=1\), \(\pi _0=2\), and \(r_1=2.8\). The replicator dynamics is solved starting from homogeneous initial conditions and simulations are performed starting from random assignment of strategies.
