Research of Cooperation in Public Goods Game Based on Dynamic Network Topology Structure

Population structure is one of the important factors in cooperation behavior, which attracted lots of attention in recent years. This paper focuses on cooperation in public goods game on dynamic network topology structure, aimed at to study how population structure influenced cooperation level and the changes of population structure in game evolution. It assumed that structure update probability is bigger than strategy update probability in game evolution. Markov transition matrix is used to analysis the stochastic update of edges, combined with the method of replicator dynamics which is used to analysis the evolution of strategies. The results from theoretical analysis show that change of network structure will affect payoff matrix, leading to the change of strategies updating, the stronger link between cooperator and cooperator and the more fragile link between cooperator and defector, the easier appearance of cooperation in the population. Besides, in a reasonable range, it can be seen the larger the value of r, the higher of the cooperation level. On the other hand, as time evolves, the network structure changes from a regular nearest-neighbor coupled network to a small-world network with higher clustering coefficient and small path. The experimental results are consistent with theoretical analysis results. This study provides a new way to cooperation research with the co-evolution of structure and strategies in spatial public good games.