A characterization of absorbing sets in coalition formation games

TL;DR

This paper characterizes absorbing sets in coalition formation games using a simplified 'reduced form' and explores their implications for convergence to stability in economic environments.

Contribution

It introduces a novel characterization of absorbing sets via a small collection of coalition sets, simplifying analysis in coalition formation games.

Findings

Absorbing sets can be described using a small collection of coalition sets.

The characterization aids in understanding convergence to stability.

Applications to economic environments demonstrate the practical relevance.

Abstract

Given a standard myopic dynamic process among coalition structures, an absorbing set is a minimal collection of such structures that is never left once entered through that process. Absorbing sets are an important solution concept in coalition formation games, but they have drawbacks: they can be large and hard to obtain. In this paper, we characterize an absorbing set in terms of a collection consisting of a small number of sets of coalitions that we refer to as a "reduced form" of a game. We apply our characterization to study convergence to stability in several economic environments.