An Empirical Distribution of the Number of Subsets in the Core Partitions of Hedonic Games

A Monte Carlo method was used in this paper to investigate the properties of hedonic games. Hedonic games or coalition formation games are important in cooperative game theory because their focus is on modeling individual’s preferences, and they have been applied in practical problems. Finding theoretical properties of hedonic games analytically is difficult for complex games. Monte Carlo methods can be used to stochastically generate empirical distributions to gain insight into theoretical properties. In this paper, the focus is on investigating the properties of hedonic games using Monte Carlo methods, specifically, the distribution of the number of subsets in the core partitions of hedonic games. The set of core partitions are the hedonic games equivalent to the core. The distribution of the number of subsets in a core partition can give insight into the probabilities of occurrence of different possible coalitions in the core partitions of hedonic games. This information may help a modeler to build a more efficient social model when there exists a hedonic game scenario. By solving millions of hedonic games numerically, using Monte Carlo methods, it was found that the number of subsets in the core of hedonic games approximately follows the normal distribution instead of the expected distribution generated by Stirling’s partition number.