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The general graph matching game: Approximate core

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  • Vazirani, Vijay V.

Abstract

The classic paper of Shapley and Shubik (1971) characterized the core of the assignment game using ideas from matching theory and LP-duality theory and their highly non-trivial interplay. Whereas the core of this game is always non-empty, that of the general graph matching game can be empty.

Suggested Citation

  • Vazirani, Vijay V., 2022. "The general graph matching game: Approximate core," Games and Economic Behavior, Elsevier, vol. 132(C), pages 478-486.
    • Handle: RePEc:eee:gamebe:v:132:y:2022:i:c:p:478-486
    DOI: 10.1016/j.geb.2022.01.017
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    References listed on IDEAS

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    Cited by:

    1. Vijay V. Vazirani, 2022. "Cores of Games via Total Dual Integrality, with Applications to Perfect Graphs and Polymatroids," Papers 2209.04903, arXiv.org, revised Nov 2022.
    2. Tianhang Lu & Han Xian & Qizhi Fang, 2023. "Approximate Core Allocations for Edge Cover Games," Papers 2308.11222, arXiv.org.
    3. Vijay V. Vazirani, 2022. "New Characterizations of Core Imputations of Matching and $b$-Matching Games," Papers 2202.00619, arXiv.org, revised Dec 2022.
    4. Vijay V. Vazirani, 2023. "LP-Duality Theory and the Cores of Games," Papers 2302.07627, arXiv.org, revised Mar 2023.

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    More about this item

    Keywords

    Assignment game; General graph matching game; Core; Approximate core; Transferable utility (TU) market; LP-duality;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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