Memory-based snowdrift game on networks

Abstract

We present a memory-based snowdrift game (MBSG) taking place on networks. We found that, when a lattice is taken to be the underlying structure, the transition of spatial patterns at some critical values of the payoff parameter is observable for both 4 and 8-neighbor lattices. The transition points as well as the styles of spatial patterns can be explained by local stability analysis. In sharp contrast to previously reported results, cooperation is promoted by the spatial structure in the MBSG. Interestingly, we found that the frequency of cooperation of the MBSG on a scale-free network peaks at a specific value of the payoff parameter. This phenomenon indicates that properly encouraging selfish behaviors can optimally enhance the cooperation. The memory effects of individuals are discussed in detail and some non-monotonous phenomena are observed on both lattices and scale-free networks. Our work may shed some new light on the study of evolutionary games over networks.

Evolutionary mixed games in structured populations: Cooperation and the benefits of heterogeneity

“…Despite its simplicity, however, the iterated prisoner's dilemma game continues to inspire research across the social and natural sciences [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27]. If the ranking of the payoffs is changed, other social dilemmas, such as the snowdrift game for T > R > S > P , are obtained, which has also received substantial attention in the recent past [28][29][30][31][32][33][34].…”

Motion depending on the strategies of players enhances cooperation in a co-evolutionary prisoner's dilemma game

“…Since the seminal work of Nowak and May [2], evolutionary PDG in spatial networks such as square lattices [3]- [5], regular random networks [6], small-world networks [7]- [9] and scale-free networks [10]- [14] has been an important mechanism for explaining the emergence of cooperation in a population of selfish individuals. In particular, scale-free networks in which individuals' degrees exhibit high heterogeneity have a strong effect on facilitating the evolution of cooperation.…”

Evolutionary games played by multi-agent system with different memory capacity

“…Studies referring to memory propose that historic memory can be implemented by featuring players by a summary of their previous winnings and choices. Various models [36][37][38][39][40][41][42][43], where the effects of full or discounted memory are assessed, have suggested that memory can influence the emergence of cooperation for self-interested agents under suitable conditions.…”

“…They get the conclusion that memory notably stimulates cooperation in the PDG played in ordered lattices, but fails to boost cooperation as the wiring network becomes highly disordered. Further, in the work of reference [42] about the memory-based snowdrift game in networks, the assumption is that by comparing the virtual payoff (by selfquestioning) with the actual payoff, each player can get her optimal strategy corresponding to the highest payoff and then record it into her memory. In reference [43], the authors assume that individuals' performance is evaluated in terms of the accumulative payoffs in their memories.…”