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Stable sets in one-seller assignment games

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  • Dezső Bednay

Abstract

We consider von Neumann–Morgenstern stable sets in assignment games with one seller and many buyers. We prove that a set of imputations is a stable set if and only if it is the graph of a certain type of continuous and monotone function. This characterization enables us to interpret the standards of behavior encompassed by the various stable sets as possible outcomes of well-known auction procedures when groups of buyers may form bidder rings. We also show that the union of all stable sets can be described as the union of convex polytopes all of whose vertices are marginal contribution payoff vectors. Consequently, each stable set is contained in the Weber set. The Shapley value, however, typically falls outside the union of all stable sets. Copyright Springer Science+Business Media New York 2014

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  • Dezső Bednay, 2014. "Stable sets in one-seller assignment games," Annals of Operations Research, Springer, vol. 222(1), pages 143-152, November.
    • Handle: RePEc:spr:annopr:v:222:y:2014:i:1:p:143-152:10.1007/s10479-013-1439-8
    DOI: 10.1007/s10479-013-1439-8
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    References listed on IDEAS

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    1. Núñez, Marina & Rafels, Carles, 2013. "Von Neumann–Morgenstern solutions in the assignment market," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1282-1291.
    2. Schotter, Andrew, 1974. "Auctioning Böhm-Bawerk’s Horses," Working Papers 74-11, C.V. Starr Center for Applied Economics, New York University.
    3. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 177-185.
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    Cited by:

    1. 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.
    2. Trine Platz & Herbert Hamers, 2015. "On games arising from multi-depot Chinese postman problems," Annals of Operations Research, Springer, vol. 235(1), pages 675-692, December.
    3. Bando, Keisuke & Kawasaki, Ryo, 2021. "Stability properties of the core in a generalized assignment problem," Games and Economic Behavior, Elsevier, vol. 130(C), pages 211-223.
    4. R. Branzei & E. Gutiérrez & N. Llorca & J. Sánchez-Soriano, 2021. "Does it make sense to analyse a two-sided market as a multi-choice game?," Annals of Operations Research, Springer, vol. 301(1), pages 17-40, June.

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