The coevolving behavior of games and strategies under different network structures

Abstract

In this paper, we study the coevolving behavior of mixed games when agents have a relationship represented by a fully connected network or a square lattice. Under the imitation update rule, whether the system will evolve to a state of pure game or mixed games and what the level of cooperation of the population will finally be are dependent on the initial fraction of mixed games, the game parameters and the network structures. We find that agents prefer to afford the prisoner’s dilemma (PD) game than the snowdrift game in the full connected network or in the square lattice and thus the cooperation is greatly suppressed. When the PD game mixes with the stag hunt game initially, they will coexist during evolution and a bistable phenomenon is observed. Meanwhile, the fraction of cooperation is enhanced when agents compete in a square lattice by comparison with the case of a fully connected network. If the PD game mixes with the harmony game (HG) initially, which one will dominate the other is related to the game parameters. The cooperation prevails in the population if the HG dominates the PD game. We also analyze the case of a fully connected network by a theory and the theoretical results are in good agreement with the simulation data.