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.
- [1] . 1995. Paths to marriage stability. Discrete Applied Mathematics 63, 1 (1995), 1–12.Google ScholarDigital Library
- [2] . 2019. Fractional hedonic games. ACM Transactions on Economics and Computation 7, 2 (2019), 1–29.Google ScholarDigital Library
- [3] . 2016. Boolean hedonic games. In Proceedings of the 15th International Conference on Principles of Knowledge Representation and Reasoning (KR’16). 166–175.Google Scholar
- [4] . 2016. Hedonic games. In Handbook of Computational Social Choice, , , , , and (Eds.). Cambridge University Press, 356–376.Google Scholar
- [5] . 2004. NP-completeness in hedonic games. Games and Economic Behavior 49, 1 (2004), 1–30.Google ScholarCross Ref
- [6] . 2001. Core in a simple coalition formation game. Social Choice and Welfare 18 (2001), 135–153.Google ScholarCross Ref
- [7] . 2003. Approximation Hardness of Short Symmetric Instances of MAX-3SAT.
Technical Report TR03-049. Electronic Colloquium on Computational Complexity (ECCC).Google Scholar - [8] . 2018. Nash stable outcomes in fractional hedonic games: Existence, efficiency and computation. Journal of Artificial Intelligence Research 62 (2018), 315–371.Google ScholarDigital Library
- [9] . 1948. On the rationale of group decision-making. Journal of Political Economy 56, 1 (1948), 23–34.Google ScholarCross Ref
- [10] . 2023. Causes of stability in dynamic coalition formation. In Proceedings of the 37th AAAI Conference on Artificial Intelligence (AAAI’23).
Forthcoming .Google Scholar - [11] . 2020. Individual-based stability in hedonic diversity games. In Proceedings of the 34th AAAI Conference on Artificial Intelligence (AAAI’20). 1822–1829.Google ScholarCross Ref
- [12] . 2002. The stability of hedonic coalition structures. Games and Economic Behavior 38, 2 (2002), 201–230.Google ScholarCross Ref
- [13] . 2015. Fractional hedonic games: Individual and group stability. In Proceedings of the 14th International Conference on Autonomous Agents and Multiagent Systems (AAMAS’15). 1219–1227.Google Scholar
- [14] . 2022. Single-agent dynamics in additively separable hedonic games. In Proceedings of the 36th AAAI Conference on Artificial Intelligence (AAAI’22). 4867–4874.Google ScholarCross Ref
- [15] . 2021. Reaching individually stable coalition structures in hedonic games. In Proceedings of the 35th AAAI Conference on Artificial Intelligence (AAAI’21). 5211–5218.Google ScholarCross Ref
- [16] . 2019. On the convergence of swap dynamics to Pareto-optimal matchings. In Proceedings of the 15th International Conference on Web and Internet Economics (WINE’19). 100–113.Google ScholarCross Ref
- [17] . 2019. Hedonic diversity games. In Proceedings of the 18th International Conference on Autonomous Agents and Multiagent Systems (AAMAS’19). 565–573.Google ScholarDigital Library
- [18] . 2023. Topological distance games. In Proceedings of the 37th AAAI Conference on Artificial Intelligence (AAAI’23).
Forthcoming .Google Scholar - [19] . 2019. Local core stability in simple symmetric fractional hedonic games. In Proceedings of the 18th International Conference on Autonomous Agents and Multiagent Systems (AAMAS’19). 574–582.Google ScholarDigital Library
- [20] . 2019. On hedonic games with common ranking property. In Proceedings of the 11th International Conference on Algorithms and Complexity (CIAC’19). 137–148.Google ScholarDigital Library
- [21] . 2001. Stability in coalition formation games. International Journal of Game Theory 29 (2001), 487–494.Google Scholar
- [22] . 1980. Hedonic coalitions: Optimality and stability. Econometrica 48, 4 (1980), 987–1003.Google ScholarCross Ref
- [23] . 2021. Relaxed core stability in fractional hedonic games. In Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI’21). 182–188.Google ScholarCross Ref
- [24] . 1988. Partnerships. Quarterly Journal of Economics 103 (1988), 279–297.Google ScholarCross Ref
- [25] . 2019. Computing stable outcomes in symmetric additively separable hedonic games. Mathematics of Operations Research 44, 3 (2019), 1101–1121.Google ScholarCross Ref
- [26] . 2018. Dynamics in matching and coalition formation games with structural constraints. Artificial Intelligence 262 (2018), 222–247.Google ScholarDigital Library
- [27] . 1972. Reducibility among combinatorial problems. In Complexity of Computer Computations, and (Eds.). Plenum Press, 85–103.Google Scholar
- [28] . 2016. Complexity of hedonic games with dichotomous preferences. In Proceedings of the 30th AAAI Conference on Artificial Intelligence (AAAI’16). 579–585.Google Scholar
- [29] . 1990. Random paths to stability in two-sided matching. Econometrica 58, 6 (1990), 1475–1480.Google ScholarCross Ref
- [30] . 2015. Individual and group stability in neutral restrictions of hedonic games. Mathematical Social Sciences 78 (2015), 1–5.Google ScholarCross Ref
- [31] . 2010. Computational complexity in additive hedonic games. European Journal of Operational Research203, 3 (2010), 635–639.Google ScholarCross Ref
Index Terms
- Reaching Individually Stable Coalition Structures
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