Formation of coalition structures as a non-cooperative game 1: theory

TL;DR

This paper introduces a novel non-cooperative game framework for coalition formation that incorporates a coalition structure formation mechanism, allowing for equilibrium analysis with externalities and size restrictions.

Contribution

It develops a new non-cooperative game model with a coalition formation mechanism, embedding partition-specific strategies and payoffs, and proves the existence of equilibrium in mixed strategies.

Findings

Existence of equilibrium in mixed strategies for the family of games.

The model captures externalities within and between coalitions.

It generalizes traditional coalition concepts beyond the Shapley value.

Abstract

The paper defines a non-cooperative simultaneous finite game to study coalition structure formation with intra and inter-coalition externalities. The novelty of the game is that the game definition embeds a \textit{coalition structure formation mechanism}. This mechanism portions a set of strategies of the game into partition-specific strategy domains, what makes every partition to be a non-cooperative game with partition-specific payoffs for every player. The mechanism includes a maximum coalition size, a set of eligible partitions with coalitions sizes no greater than this number (which also serves as a restriction for a maximum number of deviators) and a coalition structure formation rule. The paper defines a family of nested non-cooperative games parametrized by a size of a maximum coalition size. Every game in the family has an equilibrium in mixed strategies. The equilibrium can generate more than one coalition and encompasses intra and inter group externalities, what makes it different from the Shapley value. Presence of individual payoff allocation makes it different from a strong Nash, coalition-proof equilibrium, and some other equilibrium concepts. The accompanying papers demonstrate applications of the proposed toolkit.