Formation of coalition structures as a non-cooperative game

TL;DR

This paper introduces a family of nested non-cooperative games that model coalition formation with externalities, providing a framework that always admits mixed equilibria and differs from classical cooperative solution concepts.

Contribution

It develops a novel non-cooperative game model for coalition structure formation using Young diagrams and introduces stability criteria, expanding the understanding of coalition dynamics.

Findings

Mixed equilibria always exist in the model

The model generalizes Nash equilibrium and differs from classical cooperative solutions

Coalition structures are described by Young diagrams

Abstract

We study coalition structure formation with intra and inter-coalition externalities in the introduced family of nested non-cooperative simultaneous finite games. A non-cooperative game embeds a coalition structure formation mechanism, and has two outcomes: an allocation of players over coalitions and a payoff for every player. Coalition structures of a game are described by Young diagrams. They serve to enumerate coalition structures and allocations of players over them. For every coalition structure a player has a set of finite strategies. A player chooses a coalition structure and a strategy. A (social) mechanism eliminates conflicts in individual choices and produces final coalition structures. Every final coalition structure is a non-cooperative game. Mixed equilibrium always exists and consists of a mixed strategy profile, payoffs and equilibrium coalition structures. We use a maximum coalition size to parametrize the family of the games. The non-cooperative game of Nash is a partial case of the model. The result is different from the Shapley value, a strong Nash, coalition-proof equilibria, core solutions, and other equilibrium concepts. We supply few non-cooperative coalition structure stability criteria.