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

Andrew J. Collins, Sheida Etemadidavan () and Wael Khallouli ()
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Andrew J. Collins: Department of Engineering Management & Systems Engineering, Batten College of Engineering & Technology, Old Dominion University, 2101 Engineering Systems Building, Norfolk, VA 23529, USA
Sheida Etemadidavan: Department of Engineering Management & Systems Engineering, Batten College of Engineering & Technology, Old Dominion University, 2101 Engineering Systems Building, Norfolk, VA 23529, USA
Wael Khallouli: Department of Engineering Management & Systems Engineering, Batten College of Engineering & Technology, Old Dominion University, 2101 Engineering Systems Building, Norfolk, VA 23529, USA

International Game Theory Review (IGTR), 2022, vol. 24, issue 03, 1-28

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.

Keywords: Cooperative game theory; hedonic games; Monte Carlo methods; core partition; core stability (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0219198922500013

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