Generating Empirical Core Size Distributions of Hedonic Games Using a Monte Carlo Method

Abstract

Hedonic games have gained popularity over the last two decades, leading to several research articles that have used analytical methods to understand their properties better. In this paper, a Monte Carlo method, a numerical approach, is used instead. Our method includes a technique for representing, and generating, random hedonic games. We were able to create and solve, using core stability, millions of hedonic games with up to 16 players. Empirical distributions of the hedonic games’ core sizes were generated, using our results, and analyzed for games of up to 13 players. Results from games of 14–16 players were used to validate our research findings. Our results indicate that core partition size might follow the gamma distribution for games with a large number of players.

Humans and the core partition: An agent-based modeling experiment

“…A core partition is a covering set of disjoint coalitions where no subset of players has an incentive to form a new coalition [ 3 , 4 ]. As with the core, it is not necessarily unique, and there is no guarantee of existence; it has been shown numerically that many hedonic games without core partitions exist [ 26 ]. The core partitions for the glove games, considered in our experiment, are determined by hand calculation; the games are purposely created to have non-empty cores.…”