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Assignment Situations With Multiple Ownership And Their Games

Author

Listed:
  • 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 ofk-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 ofk-AMO games.

Suggested Citation

  • Silvia Miquel & Bas Van Velzen & Herbert Hamers & Henk Norde, 2009. "Assignment Situations With Multiple Ownership And Their Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-13.
    • Handle: RePEc:wsi:igtrxx:v:11:y:2009:i:01:n:s021919890900211x
    DOI: 10.1142/S021919890900211X
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    Citations

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    Cited by:

    1. Arantza (M.A.) Estevez-Fernandez & Herbert Hamers, 2018. "Chinese postman games with repeated players," Tinbergen Institute Discussion Papers 18-081/II, Tinbergen Institute.
    2. Estévez-Fernández, Arantza & Hamers, Herbert, 2020. "Chinese postman games with multi-located players," European Journal of Operational Research, Elsevier, vol. 285(2), pages 458-469.

    More about this item

    Keywords

    Assignment situations; matchings; assignment games; balancedness;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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