Group-size dependent synergy in heterogeneous populations

Abstract

When people collaborate, they expect more in return than a simple sum of their efforts. This observation is at the heart of the so-called public goods game, where the participants' contributions are multiplied by an $r$ synergy factor before they are distributed among group members. However, a larger group could be more effective, which can be described by a larger synergy factor. To elaborate on the possible consequences, in this study, we introduce a model where the population has different sizes of groups, and the applied synergy factor depends on the size of the group. We examine different options when the increment of $r$ is linear, slow, or sudden, but in all cases, the cooperation level is higher than that in a population where the homogeneous $r$ factor is used. In the latter case, smaller groups perform better; however, this behavior is reversed when synergy increases for larger groups. Hence, the entire community benefits because larger groups are rewarded better. Notably, a similar qualitative behavior can be observed for other heterogeneous topologies, including scale-free interaction graphs.

9 pages, 6 figures, accepted by Chaos, Solitons and Fractals: the Interdisciplinary Journal of Nonlinear Science, and Nonequilibrium and Complex Phenomena

References in corpus (16)

• Evolutionary games on graphs
• Statistical physics of human cooperation
• Evolutionary dynamics of group interactions on structured populations: A review
• Social diversity and promotion of cooperation in the spatial prisoner's dilemma game
• Towards effective payoffs in the prisoner's dilemma game on scale-free networks
• If players are sparse social dilemmas are too: Importance of percolation for evolution of cooperation
• Impact of critical mass on the evolution of cooperation in spatial public goods games
• Percolation threshold determines the optimal population density for public cooperation
• Dynamically generated cyclic dominance in spatial prisoner's dilemma games
• A double-edged sword: Benefits and pitfalls of heterogeneous punishment in evolutionary inspection games
• Accuracy in strategy imitations promotes the evolution of fairness in the spatial ultimatum game
• Blocking defector invasion by focusing on the most successful partner
• Tactical cooperation of defectors in a multi-stage public goods game
• Effects of income redistribution on the evolution of cooperation in spatial public goods games
• Symbiotic behaviour in the Public Goods game with altruistic punishment
• Small Fraction of Selective Cooperators Can Elevate General Wellbeing Significantly

Cited by in corpus (5)

• Evolutionary dynamics in state-feedback public goods games with peer punishment
• Heterogeneous contributions can jeopardize cooperation in the Public Goods Game
• Drivers of cooperation in social dilemmas on higher-order networks
• Reputation assimilation mechanism for sustaining cooperation
• Evolutionary dynamics in public goods games with general frequency-dependent returns