用蒙特卡罗方法生成享乐博弈的经验核心规模分布
Generating Empirical Core Size Distributions of Hedonic Games using a Monte Carlo Method
摘要：
数据分析允许分析人员通过使用各种计算方法（包括蒙特卡罗方法）来深入了解潜在人群。本文讨论了一种将蒙特卡罗方法应用于享乐博弈的方法。在过去的二十年里，享乐游戏越来越受欢迎，导致了一些研究文章，这些文章关注核心分区存在的必要条件，充分条件或两者兼而有之。研究人员在这项工作中使用了分析方法。我们建议使用数值方法将提供通过当前分析方法可能无法获得的见解。在本文中，我们描述了一种方法来表示享乐游戏，严格的偏好，在一个矩阵的形式，可以很容易地生成，也就是说，随机生成的偏好，为每个玩家的享乐游戏。使用这种生成方法，我们能够创建和解决，即，找到数百万个享乐博弈的核心分区我们的蒙特卡罗实验生成了最多13个玩家的游戏。结果讨论了局中人数一定时的对策核心规模的分布形式。我们还讨论了计算的考虑。我们对享乐博弈的数值研究揭示了享乐博弈的基本性质。
英文摘要：
Data analytics allows an analyst to gain insight into underlying populations through the use of various computational approaches, including Monte Carlo methods. This paper discusses an approach to apply Monte Carlo methods to hedonic games. Hedonic games have gain popularity over the last two decades leading to several research articles that are concerned with the necessary, sufficient, or both conditions of the existence of a core partition. Researchers have used analytical methods for this work. We propose that using a numerical approach will give insights that might not be available through current analytical methods. In this paper, we describe an approach to representing hedonic games, with strict preferences, in a matrix form that can easily be generated; that is, a hedonic game with randomly generated preferences for each player. Using this generative approach, we were able to create and solve, i.e., find any core partitions, of millions of hedonic games. Our Monte Carlo experiment generated games with up to thirteen players. The results discuss the distribution form of the core size of the games of a given number of players. We also discuss computational considerations. Our numerical study of hedonic games gives insight into the underlying properties of hedonic games.
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