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 paper, 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 (2002), Brandl et al. (2005), and Boehmer and Elkind (2020).
翻译:对多试剂系统中联盟形成的正式研究通常在来自经济理论的超音速游戏框架内实现,这一研究领域的主要重点是确定是否存在符合各种稳定标准的联盟结构及其计算复杂性。根据个人行为形成联盟的实际过程没有引起多少注意。在本文中,我们研究在各种既定的超音速游戏类别中,包括匿名、双声、分声、分声和超音量多样性游戏中,导致稳定分化的简单动态的趋同。我们认为,这种动态的基础是个人稳定:如果一个代理人比较好,就会加入另一个联盟,而没有友好联盟的成员则更糟糕。我们的结果有三重。首先,我们确定我们动态(快)融合的条件。为此,我们开发了基于同时使用多重相互交织的潜在功能的新技术,并建立了一种减少发现匿名超音速游戏和超音量多样性游戏之间密切关系的特性。第二,我们提供了详细的反比标准,确定个人稳定分界。第三,我们研究了(20世纪) 和BA型动态的计算复杂性,我们建议解决了BA型和BA型 20 的形成。