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

Abstract

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.

Scale-free networks may not necessarily witness cooperation

“…Apart from game rules, the underlying structure of the population also plays an essential role in the outcome of the game [11][12][13][14][15][16][17][18]. The underlying graph topology imparts spatial restrictions on the interactions between players.…”

“…Assortativity among cooperators, r C , can perhaps be differently scrutinised through the "cooperator graph", G C , instead of the original graph, G [17]. Similarly, the "defector graph", G D , may be useful to understand the assortativity between defectors, r D .…”

“…Similarly, the "defector graph", G D , may be useful to understand the assortativity between defectors, r D . We can construct G C and G D from the original graph, G [17]. G C and G D are solely graphs of cooperators and defectors, respectively, among themselves.…”

“…We review the correlation of assortativity among cooperators and maintenance of cooperation. For this we borrow the notion of "cooperator graph", G C , and "defector graph", G D [17]. We measure assortativity between cooperators, r C , through the help of G C .…”

Deterministic and stochastic cooperation transitions in evolutionary games on networks

“…Since that seminal work by Nowak and May [8] and with the rapid development of the complex networks field in the last few decades [13][14][15], a lot of research has been focused on the role of the underlying network topology in the emergence of cooperation, including aspects like network heterogeneity both theoretically [16,17] and experimentally [18][19][20][21], the presence of a layered structure de- * nagi.khalil@urjc.es scribing the different types of social relationships [22,23] and degree correlations among layers [24], or game refinements by introducing topology dependent payoffs [25] and the influence of an update rule and connectivity on the outcome dynamics of structured populations [26,27].…”