On Existence of Equilibrium Under Social Coalition Structures

TL;DR

This paper introduces new equilibrium concepts based on social coalition restrictions in strategic games, analyzing their existence in resource selection games with practical implications for social and institutional constraints.

Contribution

It proposes novel equilibrium notions influenced by social coalition structures and provides comprehensive existence results for resource selection games.

Findings

New equilibrium notions under social coalition restrictions

Complete existence and non-existence results for RSGs

Insights into coalition formation constraints in strategic settings

Abstract

In a strategic form game a strategy profile is an equilibrium if no viable coalition of agents (or players) benefits (in the Pareto sense) from jointly changing their strategies. Weaker or stronger equilibrium notions can be defined by considering various restrictions on coalition formation. In a Nash equilibrium, for instance, the assumption is that viable coalitions are singletons, and in a super strong equilibrium, every coalition is viable. Restrictions on coalition formation can be justified by communication limitations, coordination problems or institutional constraints. In this paper, inspired by social structures in various real-life scenarios, we introduce certain restrictions on coalition formation, and on their basis we introduce a number of equilibrium notions. As an application we study our equilibrium notions in resource selection games (RSGs), and we present a complete set of existence and non-existence results for general RSGs and their important special cases.