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The minimum set of $$\mu $$ μ -compatible subgames for obtaining a stable set in an assignment game

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  • Keisuke Bando

    (Shinshu University)

  • Yakuma Furusawa

    (Tokyo Institute of Technology)

Abstract

This study analyzes von Neumann-Morgenstern stable sets in an assignment game. Núñez and Rafels (2013) have shown that the union of the extended cores of all $$\mu $$ μ -compatible subgames is a stable set. Typically, the set of all $$\mu $$ μ -compatible subgames includes many elements, most of which are inessential for obtaining the stable set. We provide an algorithm to find a set of $$\mu $$ μ -compatible subgames for obtaining the stable set when the valuation matrix is positive. Moreover, this algorithm finds the minimum set of $$\mu $$ μ -compatible subgames for obtaining the stable set when each column and row in the valuation matrix is constituted from different positive numbers. Our simulation result reveals that the average size of the minimum set of $$\mu $$ μ -compatible subgames for obtaining the stable set is significantly lower than that of the set of all $$\mu $$ μ -compatible subgames.

Suggested Citation

  • Keisuke Bando & Yakuma Furusawa, 2023. "The minimum set of $$\mu $$ μ -compatible subgames for obtaining a stable set in an assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 231-252, March.
    • Handle: RePEc:spr:jogath:v:52:y:2023:i:1:d:10.1007_s00182-022-00816-1
    DOI: 10.1007/s00182-022-00816-1
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