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Reaching Individually Stable Coalition Structures

Reaching Individually Stable Coalition Structures The formal study of coalition formation in multi-agent systems is typically realized in the framework of hedonic games, which originate from economic theory. The main focus of this branch of research has been on the existence and the computational complexity of deciding the existence of coalition structures that satisfy various stability criteria. The actual process of forming coalitions based on individual behavior has received little attention. In this article, we study the convergence of simple dynamics leading to stable partitions in a variety of established classes of hedonic games, including anonymous, dichotomous, fractional, and hedonic diversity games. The dynamics we consider is based on individual stability: an agent will join another coalition if she is better off and no member of the welcoming coalition is worse off. Our results are threefold. First, we identify conditions for the (fast) convergence of our dynamics. To this end, we develop new techniques based on the simultaneous usage of multiple intertwined potential functions and establish a reduction uncovering a close relationship between anonymous hedonic games and hedonic diversity games. Second, we provide elaborate counterexamples determining tight boundaries for the existence of individually stable partitions. Third, we study the computational complexity of problems related to the coalition formation dynamics. In particular, we settle open problems suggested by Bogomolnaia and Jackson, Brandl et al., and Boehmer and Elkind. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Economics and Computation Association for Computing Machinery

Reaching Individually Stable Coalition Structures

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References (32)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2023 Copyright held by the owner/author(s). Publication rights licensed to ACM.
ISSN
2167-8375
eISSN
2167-8383
DOI
10.1145/3588753
Publisher site
See Article on Publisher Site

Abstract

The formal study of coalition formation in multi-agent systems is typically realized in the framework of hedonic games, which originate from economic theory. The main focus of this branch of research has been on the existence and the computational complexity of deciding the existence of coalition structures that satisfy various stability criteria. The actual process of forming coalitions based on individual behavior has received little attention. In this article, we study the convergence of simple dynamics leading to stable partitions in a variety of established classes of hedonic games, including anonymous, dichotomous, fractional, and hedonic diversity games. The dynamics we consider is based on individual stability: an agent will join another coalition if she is better off and no member of the welcoming coalition is worse off. Our results are threefold. First, we identify conditions for the (fast) convergence of our dynamics. To this end, we develop new techniques based on the simultaneous usage of multiple intertwined potential functions and establish a reduction uncovering a close relationship between anonymous hedonic games and hedonic diversity games. Second, we provide elaborate counterexamples determining tight boundaries for the existence of individually stable partitions. Third, we study the computational complexity of problems related to the coalition formation dynamics. In particular, we settle open problems suggested by Bogomolnaia and Jackson, Brandl et al., and Boehmer and Elkind.

Journal

ACM Transactions on Economics and Computation – Association for Computing Machinery

Published: Jun 24, 2023

Keywords: Coalition formation

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