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

TL;DR

This paper introduces a Monte Carlo simulation approach to analyze the distribution of core sizes in hedonic games with strict preferences, providing insights beyond traditional analytical methods.

Contribution

It presents a novel numerical method for generating and analyzing large sets of hedonic games, revealing core size distributions through extensive simulations.

Findings

Core size distributions vary with the number of players.

Monte Carlo methods enable analysis of millions of games.

Insights into properties of hedonic games beyond analytical solutions.

Abstract

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.