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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Andrew J. Collins & Sheida Etemadidavan & Wael Khallouli, 2022. "Generating Empirical Core Size Distributions of Hedonic Games Using a Monte Carlo Method," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 24(03), pages 1-28, September.
    • Handle: RePEc:wsi:igtrxx:v:24:y:2022:i:03:n:s0219198922500013
    DOI: 10.1142/S0219198922500013
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    Cited by:

    1. Sheida Etemadidavan & Andrew J. Collins, 2021. "An Empirical Distribution of the Number of Subsets in the Core Partitions of Hedonic Games," SN Operations Research Forum, Springer, vol. 2(4), pages 1-20, December.

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