Spatial snowdrift game of a heterogeneous agent system: cooperative behavior

We study the cooperative behavior of an evolutionary snowdrift game in a heterogeneous system with two types of agents, in which the inner-directed agents adopt the memory-based updating rule while the copycat-like ones take the unconditional imitation rule. The equilibrium cooperation frequency in such a heterogeneous system shows plateau structures with discontinuous steplike jumps as a function of the cost-to-benefit ratio, as well in homogeneous systems only with inner-directed agents [W.-X. Wang, J. Ren, G.R. Chen, B.-H. Wang, Phys. Rev. E 74, 056113 (2006)] or copycat-like ones [P.-P. Li, J. Ke, Z. Lin, P.M. Hui, Phys. Rev. E 85, 021111 (2012)]. One nontrivial feature for the heterogenous agent system is that the number of plateaux varies non-monotonically with the composition of the two mixing agents. Moreover, there exists a worst composition of the heterogeneous agents for each plateau, leading to the lowest cooperation level. We then qualitatively interpret these features by invoking the stability of local microscopic patterns. Our results are of some help in understanding the cooperative behaviors of heterogenous agent systems, and the qualitative analysis employed here also provides a useful method for studying in depth the evolutionary dynamics of spatial games.

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