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The Assignment Game : The Reduced Game

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  • Guillermo Owen

Abstract

Let v be an assignment game. For a given reference payoff vector (x; y), and a coalition S, bargaining within the coalition can be represented by either the reduced game or the derived game. It is known that the reduced game need not be an assignment game (in fact, it need not be super additive) while the derived game is another assignment game, with modified reservation prices. We prove that, when the reference vector is in the core of the game, the derived game is the super additive cover of the reduced game.

Suggested Citation

  • Guillermo Owen, 1992. "The Assignment Game : The Reduced Game," Annals of Economics and Statistics, GENES, issue 25-26, pages 71-79.
    • Handle: RePEc:adr:anecst:y:1992:i:25-26:p:71-79
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    File URL: http://www.jstor.org/stable/20075857
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    Cited by:

    1. Francesc Llerena (Universitat Rovira i Virgili - CREIP) & Marina Nunez (Universitat de Barcelona) & Carles Rafels (Universitat de Barcelona), 2012. "An axiomatization of the nucleolus of the assignment game," Working Papers in Economics 286, Universitat de Barcelona. Espai de Recerca en Economia.
    2. Domènech, Gerard & Núñez, Marina, 2022. "Axioms for the optimal stable rules and fair-division rules in a multiple-partners job market," Games and Economic Behavior, Elsevier, vol. 136(C), pages 469-484.
    3. Gerichhausen, Marloes & Hamers, Herbert, 2009. "Partitioning sequencing situations and games," European Journal of Operational Research, Elsevier, vol. 196(1), pages 207-216, July.
    4. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    5. Marina Nunez Oliva & Carlos Rafels Pallarola, 2001. "The extreme core allocations of the assignment game," Working Papers in Economics 65, Universitat de Barcelona. Espai de Recerca en Economia.
    6. Marina Núñez & Tamás Solymosi, 2017. "Lexicographic allocations and extreme core payoffs: the case of assignment games," Annals of Operations Research, Springer, vol. 254(1), pages 211-234, July.
    7. van den Brink, René & Núñez, Marina & Robles, Francisco, 2021. "Valuation monotonicity, fairness and stability in assignment problems," Journal of Economic Theory, Elsevier, vol. 195(C).
    8. Suijs, J.P.M. & Hamers, H.J.M. & Tijs, S.H., 1995. "On consistency of reward allocation rules in sequencing situations," Other publications TiSEM f4745bac-fd51-4006-9321-d, Tilburg University, School of Economics and Management.
    9. Francesc Llerena & Marina Núñez & Carles Rafels, 2015. "An axiomatization of the nucleolus of assignment markets," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(1), pages 1-15, February.
    10. Gerichhausen, M. & Hamers, H.J.M., 2007. "Partitioning Sequencing Situations and Games," Discussion Paper 2007-40, Tilburg University, Center for Economic Research.
    11. Farooq, Bilal & Miller, Eric J., 2012. "Towards integrated land use and transportation: A dynamic disequilibrium based microsimulation framework for built space markets," Transportation Research Part A: Policy and Practice, Elsevier, vol. 46(7), pages 1030-1053.
    12. Ata Atay & Francesc Llerena & Marina Núñez, 2016. "Generalized three-sided assignment markets: core consistency and competitive prices," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 572-593, October.
    13. Gerard Domènech Gironell & Marina Núñez Oliva, 2022. "Axioms for the optimal stable rules and fair-division rules in a multiple-partners job market," UB School of Economics Working Papers 2022/419, University of Barcelona School of Economics.
    14. Oriol Tejada, 2013. "Complements and Substitutes in Generalized Multisided Assignment Economies," CER-ETH Economics working paper series 13/180, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.
    15. Nunez, Marina & Rafels, Carles, 2003. "Characterization of the extreme core allocations of the assignment game," Games and Economic Behavior, Elsevier, vol. 44(2), pages 311-331, August.
    16. Gerichhausen, M. & Hamers, H.J.M., 2007. "Partitioning Sequencing Situations and Games," Other publications TiSEM 2bddbf5c-c56d-4b10-ba47-5, Tilburg University, School of Economics and Management.

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