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Assignment Situations With Multiple Ownership And Their Games

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Author Info

  • SILVIA MIQUEL

    (Departament de Matematica, Universitat de Lleida, Spain)

  • BAS VAN VELZEN

    (Tilburg University, Department of Econometrics and OR, Tilburg, The Netherlands)

  • HERBERT HAMERS

    ()
    (Tilburg University, Department of Econometrics and OR, Tilburg, The Netherlands)

  • HENK NORDE

    (Tilburg University, Department of Econometrics and OR, Tilburg, The Netherlands)

Abstract

An assignment situation can be considered as a two-sided market consisting of two disjoint sets of objects. A non-negative reward matrix describes the profit if an object of one group is assigned to an object of the other group. Assuming that each object is owned by a different agent, Shapley and Shubik (1972) introduced a class of assignment games.This paper introduces assignment situations with multiple ownership (AMO). In these situations an object can be owned by several agents and an agent can participate in the ownership of more than one object. For AMO situations we introduce the class of k-AMO games. An AMO situation is called balanced if for any choice of the reward matrix the corresponding 1-AMO game is balanced. We provide necessary and sufficient conditions for balancedness of AMO situations. Moreover, sufficient conditions are provided for balancedness of k-AMO games.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 11 (2009)
Issue (Month): 01 ()
Pages: 1-13

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Handle: RePEc:wsi:igtrxx:v:11:y:2009:i:01:p:1-13

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Keywords: Assignment situations; matchings; assignment games; balancedness;

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  1. Solymosi, Tamas & Raghavan, Tirukkannamangai E S, 1994. "An Algorithm for Finding the Nucleolus of Asignment Games," International Journal of Game Theory, Springer, vol. 23(2), pages 119-43.
  2. T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer, vol. 30(2), pages 177-185.
  3. 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.
  4. Quint, Thomas, 1991. "Characterization of Cores of Assignment Games," International Journal of Game Theory, Springer, vol. 19(4), pages 413-20.
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