Evolutionary multiplayer games on graphs with edge diversity

Abstract

Evolutionary game dynamics in structured populations has been extensively explored in past decades. However, most previous studies assume that payoffs of individuals are fully determined by the strategic behaviors of interacting parties, and social ties between them only serve as the indicator of the existence of interactions. This assumption neglects important information carried by inter-personal social ties such as genetic similarity, geographic proximity, and social closeness, which may crucially affect the outcome of interactions. To model these situations, we present a framework of evolutionary multiplayer games on graphs with edge diversity, where different types of edges describe diverse social ties. Strategic behaviors together with social ties determine the resulting payoffs of interactants. Under weak selection, we provide a general formula to predict the success of one behavior over the other. We apply this formula to various examples which cannot be dealt with using previous models, including the division of labor and relationship- or edge-dependent games. We find that labor division can promote collective cooperation markedly. The evolutionary process based on relationship-dependent games can be approximated by interactions under a transformed and unified game. Our work stresses the importance of social ties and provides effective methods to reduce the calculating complexity in analyzing the evolution of realistic systems.

Evolutionary dynamics with game transitions

“…Recent years have seen a growing interest in exploring evolutionary dynamics in a changing and/or heterogeneous environments (41–50). Our model is somewhat different.…”

Diverse strategic identities induce dynamical states in evolutionary games

“…Our approach is in line with a stream of recent research where edges (rather than vertices) are the centers of evolutionary dynamics [43][44][45][46][47]. In particular, Ref.…”

“…[46] assumes that the edge strategy (cooperation or defection) yielding a higher payoff is likely to replace strategies producing lower payoffs, and shows that this mechanism generally supports cooperation. Reference [47] extends the idea of edges being the centers of evolutionary dynamics by suggesting that edges may also convey additional information, such as genetic similarity, geographic proximity, and social closeness. Moreover, Ref.…”

Evolution of cooperation with joint liability

“…Examples of collective reputation are ubiquitous, such as a product's brand and a student's diploma, both serving as a credit certification of their qualities and abilities. Besides, to some degree, joint liability is analogous to the threshold public goods game, in which the total contribution into the common pool must exceed a threshold such that each individual can benefit from the public goods [45][46][47]. In other words, if the number of defectors who do not contribute is above a certain threshold, none of them obtains payoff.…”