Interplay of Reward and Size of Groups in the Optional Public Goods Game

TL;DR

This paper analyzes how reward levels and group size influence the emergence and stability of cooperation in the Optional Public Goods Game through simulations, revealing various strategic coexistence and dominance scenarios.

Contribution

It provides a comprehensive analysis of the effects of reward and group size on cooperation dynamics in the optional public goods game, including conditions for strategy coexistence and dominance.

Findings

Cooperation can emerge and be sustained under certain reward and group size conditions.

Multiple equilibrium states, including coexistence and cyclic dominance, are identified.

Cycle prevalence and strategy dominance depend on key parameters like reward and group size.

Abstract

The Optional Public Goods Game is a three-strategy game in which an individual can play as a cooperator or defector or decide not to participate. Despite its simplicity, this model can effectively represent many human social dilemmas, such as those found in the use of public services, environmental concerns, or other activities related to society. In this contribution, we present a comprehensive analysis of the conditions under which spontaneous, sustained cooperation emerges and the characteristics of these cooperative states. Through simulations, we demonstrate the conditions leading to the coexistence of the three strategies in a steady equilibrium or the alternate dominance of each strategy in a rock-paper-scissors fashion. The results identify each of the possible scenarios in terms of two key parameters: the multiplication rate of the public good game (reward) and the size of the group of potential players. We also discuss other details of the game that may influence the appearance of cycles, along with relevant characteristics of these cycles, such as the prevalence of cooperation.