Evolutionary Public Goods Game on the Birandom Geometric Graph

To investigate the evolution of cooperation in spatial public goods games, this paper establishes a birandom geometric graph, in which two types of nodes, representing players and public goods respectively, are placed at random locations in the unit square. Each public good has a limit influence range and the individuals that fall into the same range engage in a public good game. In contrast to the classical network models consisting of only one type of nodes, the birandom geometric graph provides a natural way to describe the scenarios where individuals and public resources are independent of each other. Numerical simulations reveal that cooperation can be significantly promoted when the group size and the average number of groups that each player participates in are relatively small, which is at odds with the results on the square lattice, but is consistent with a body of empirical evidence reported by Ostrom and Olson et al. Analysis of the evolutionary process suggests that the facilitation of cooperation is due primarily to the formation of the cooperative clusters, which can effectively resist the invasion of the defectors.