G-games with coalitions

TL;DR

This paper introduces a framework for G-games where strategies are graph nodes, incorporating coalition dynamics, and presents equilibrium concepts, a Folk Theorem, and Markov Chain methods for analysis.

Contribution

It develops novel equilibrium concepts for G-games with coalitions, extending classical game theory to graph-structured strategies and repeated interactions.

Findings

Introduces pure and mixed equilibria for G-games

Proves a Folk Theorem for repeated G-games

Describes equilibria via Markov Chains

Abstract

This paper models games where the strategies are nodes of a graph G (we denote them as G-games) and in presence of coalition structures. The cases of one-shot and repeated games are presented. In the latter situation, coalitions are assumed to move from a strategy to another one under the constraint that they are adjacent in the graph. We introduce novel concepts of pure and mixed equilibria which are comparable with classical Nash and Berge equilibria. A Folk Theorem for G-games of repeated type is presented. Moreover, equilibria are proven to be described through suitably defined Markov Chains, hence leading to a constrained Monte Carlo Markov Chain procedure.