Coexistence of coordination and anticoordination in nonlinear public goods game

Abstract

There is a plethora of instances of interactions between players, in both biological and socio-economical context, that can be modeled as the paradigmatic PGG. However, in such interactions, arguably the PGG is often nonlinear in nature. This is because the increment in benefit generated, owing to additional cost contributed by the players, is realistically seldom linear. Furthermore, sometimes a social good is created due to interspecific interactions, e.g. in cooperative hunting by animals of two different species. In this paper, we study the evolutionary dynamics of a heterogenous population of cooperators and defectors playing nonlinear PGG; here we define heterogenous population as the one composed of distinct subpopulations with interactions among them. We employ the replicator equations for this investigation, and present the non-trivial effects of nonlinearity and size of the groups involved in the game. We report the possibility of discoordination, and coexistence of coordination and anti-coordination in such nonlinear PGG.

Keywords

• evolutionary game theory
• nonlinear public goods game
• replicator dynamics
• stability analysis
• multistability