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

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Abstract

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.

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Availability of Data and Material

The data in this research is not distributed in public due to its size, which is larger than 10 GB, but it will be available upon request.

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The code in this research is not distributed in public but will be available upon request.

Notes

  1. In glove games, players have different numbers of right-hand and/or left-hand gloves. A pair of gloves can be sold for a profit. Players should pool their gloves in a way that maximizes their own score.

  2. In the Prisoner’s Dilemma, there exist only two players (prisoners). Binding agreement and communication is not possible between the two prisoners. In addition, both prisoners know that if one confesses and the other one does not, the confessor will be freed and the other one will be jailed for 3 years. Also, both will be put in jail for 2 years; if both confess and if neither of them confesses, both will be jailed for only 1 year. Although the last option seems to be the optimum case, but this is not always the outcome of the game because players cannot communicate to bind agreement. So, this is a dilemma for both prisoners to confess or not.

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Acknowledgements

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  1. Department of Engineering Management and Systems Engineering, Batten College of Engineering and Technology, Old Dominion University, Norfolk, VA, USA

    Sheida Etemadidavan & Andrew J. Collins

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  1. Sheida Etemadidavan
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Correspondence to Sheida Etemadidavan.

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Etemadidavan, S., Collins, A.J. An Empirical Distribution of the Number of Subsets in the Core Partitions of Hedonic Games. Oper. Res. Forum 2, 65 (2021). https://doi.org/10.1007/s43069-021-00103-x

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