Topology dependent payoffs can lead to escape from prisoner’s dilemma

Evolutionary game theory attempts to understand the stability of cooperation in spatially restricted populations. Maintenance of cooperation is difficult, especially in the absence of spatial restrictions. There have been numerous studies of games played on graphs. It is well recognised that the underlying graph topology significantly influences the outcome of such games. A natural yet unexplored question is whether the topology of the underlying structures on which the games are played possess no role whatsoever in the determination of payoffs. Herein, we introduce a form of game payoff, which is weakly dependent on the underlying topology. Our approach is inspired by the well-known microbial phenomenon of quorum sensing. We demonstrate that even with such a weak dependence, the basic game dynamics and indeed the very nature of the game may be altered.