Frequency-dependent returns in nonlinear public goods games

TL;DR

This paper introduces a nonlinear public goods game model where the return depends on the number of contributors, revealing richer evolutionary dynamics and overcoming the limitations of linear models in cooperation studies.

Contribution

It presents a novel nonlinear model of public goods with a linear dependence of returns on contributors, analyzing its evolutionary implications and dynamics.

Findings

Breaks the dominance of defectors in linear models

Reveals richer dynamical outcomes in evolution

Provides microscopic derivation of evolutionary results

Abstract

When individuals interact in groups, the evolution of cooperation is traditionally modeled using the framework of public goods games. These models often assume that the return of the public good depends linearly on the fraction of contributors. In contrast, in real life public goods interactions, the return can depend on the size of the investor pool as well. Here, we consider a model in which the multiplication factor (marginal per capita return) for the public good depends linearly on how many contribute, which results in a nonlinear model of public goods. This simple model breaks the curse of dominant defection found in linear public goods interactions and gives rise to richer dynamical outcomes in evolutionary settings. We provide an in-depth analysis of the more varied decisions by the classical rational player in nonlinear public goods interactions as well as a mechanistic, microscopic derivation of the evolutionary outcomes for the stochastic dynamics in finite populations and in the deterministic limit of infinite populations. This kind of nonlinearity provides a natural way to model public goods with diminishing returns as well as economies of scale.