Culture and cooperation in a spatial public goods game

We study the coevolution of culture and cooperation by combining the Axelrod model of cultural dissemination with a spatial public goods game, incorporating both noise and social influence. Both participation and cooperation in public goods games are conditional on cultural similarity. We find that a larger “scope of cultural possibilities” in the model leads to the survival of cooperation, when noise is not present, and a higher probability of a multicultural state evolving, for low noise rates. High noise rates, however, lead to both rapid extinction of cooperation and collapse into cultural “anomie,” in which stable cultural regions fail to form. These results suggest that cultural diversity can actually be beneficial for the evolution of cooperation, but that cultural information needs to be transmitted accurately in order to maintain both coherent cultural groups and cooperation.

Figure 1

Fraction of agents which are (conditional) cooperators after ${10}^9$ steps as a function of $q$ for different noise rates. Lines are shown purely as an aid to the eye as $q$ is an integer. The dashed vertical line shows the critical value of $q$ (for zero noise).

Figure 2

Average number of players per public goods game after ${10}^9$ steps as a function of $q$ for different values of the noise rate. Lines are shown purely as an aid to the eye as $q$ is an integer. The average number of players per game is normalized by division by the maximum possible number of players, which is the number of agents in the von Neumann neighborhood of the focal agent. The dashed vertical line shows the critical value of $q$ (for zero noise).

Figure 3

Number of cultural regions (normalized by division by number of lattice sites) after ${10}^9$ steps as a function of $q$, for different values of the noise rate. Lines are shown purely as an aid to the eye as $q$ is an integer. The dashed vertical line shows the critical value of $q$ (for zero noise).

Figure 4

Average number of players per game, fraction of agents which are (conditional) cooperators, and number of cultural regions, as a function of time, for three values of $q$ and two noise rates (zero in the left column and intermediate in the right column). The average number of players per game is normalized by division by the maximum possible number of players, which is the number of agents in the von Neumann neighborhood of the focal agent.

Figure 5

Snapshot of the cultures (left) and cooperators (right) on the lattice after ${10}^9$ iterations for $r=0$ and $q=65$, top (corresponding to the end of the time series in the graph on the left of the central row in Fig. 4), and $q=95$, bottom (corresponding to the end of the time series in the graph on the bottom left in Fig. 4). Each distinct culture vector is shown in a different color in the figures on the left, and in the figures on the right (conditional) cooperators are shown in green and defectors are shown as orange. The fraction of (conditional) cooperators for $q=65$ is approximately 11% and for $q=95$ is approximately 35%.