Emergent Collaboration in Social Purpose Games

TL;DR

This paper introduces social purpose games, a class of non-cooperative games with social benefits, analyzing their equilibria, coalition stability, and application to resource management, revealing the emergence of cooperative coalitions.

Contribution

It characterizes social purpose games, proves their potential structure, analyzes equilibrium properties, and demonstrates coalition formation and stability, especially in resource management scenarios.

Findings

Existence of potential in social purpose games.

Stable coalitions of cooperators can emerge.

Application to the tragedy of the commons shows resource over-exploitation can be mitigated.

Abstract

We study a class of non-cooperative aggregative games -- denoted as \emph{social purpose games} -- in which the payoffs depend separately on a player's own strategy (individual benefits) and on a function of the strategy profile which is common to all players (social benefits) weighted by an individual benefit parameter. This structure allows for an asymmetric assessment of the social benefit across players. We show that these games have a potential and we investigate its properties. We investigate the payoff structure and the uniqueness of Nash equilibria and social optima. Furthermore, following the literature on partial cooperation, we investigate the leadership of a single coalition of cooperators while the rest of players act as non-cooperative followers. In particular, we show that social purpose games admit the emergence of a stable coalition of cooperators for the subclass of \emph{strict} social purpose games. Due to the nature of the partial cooperative leadership equilibrium, stable coalitions of cooperators reflect a limited form of farsightedness in their formation. As a particular application, we study the tragedy of the commons game. We show that there emerges a single stable coalition of cooperators to curb the over-exploitation of the resource.