A reversed form of public goods game: equivalence and difference

TL;DR

This paper introduces a reversed form of the public goods game (R-PGG), compares it to the traditional PGG across various scenarios, and explores how heterogeneity impacts cooperation differently in each game.

Contribution

It demonstrates the conditions under which R-PGG is equivalent to PGG and identifies how heterogeneity influences cooperation distinctly in the two game types.

Findings

R-PGG is equivalent to PGG in several traditional and evolutionary scenarios.

Heterogeneity impedes cooperation in R-PGG but promotes it in PGG.

Payoff functions and strategy roles differ significantly between R-PGG and PGG under diverse conditions.

Abstract

According to the public goods game (PGG) protocol, participants decide freely whether they want to contribute to a common pool or not, but the resulting benefit is distributed equally. A conceptually similar dilemma situation may emerge when participants consider if they claim a common resource but the related cost is covered equally by all group members. The latter establishes a reversed form of the original public goods game (R-PGG). In this work, we show that R-PGG is equivalent to PGG in several circumstances, starting from the traditional analysis, via the evolutionary approach in unstructured populations, to Monte Carlo simulations in structured populations. However, there are also cases when the behavior of R-PGG could be surprisingly different from the outcome of PGG. When the key parameters are heterogeneous, for instance, the results of PGG and R-PGG could be diverse even if we apply the same amplitudes of heterogeneity. We find that the heterogeneity in R-PGG generally impedes cooperation, while the opposite is observed for PGG. These diverse system reactions can be understood if we follow how payoff functions change when introducing heterogeneity in the parameter space. This analysis also reveals the distinct roles of cooperator and defector strategies in the mentioned games. Our observations may hopefully stimulate further research to check the potential differences between PGG and R-PGG due to the alternative complexity of conditions.