Assignment Situations with Multiple Ownership and their Games
AbstractAn 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 arising from these assignment situations.This paper introduces assignment situations with multiple ownership. In these situations each object can be owned by several agents and each agent can participate in the ownership of more than one object.In this paper we study simple assignment games and relaxations that arise from assignment situations with multiple ownership.First, necessary and sufficient conditions are provided for balanced assignment situations with multiple ownership.An assignment situation with multiple ownership is balanced if for any choice of the reward matrix the corresponding simple assignment game is balanced.Second, balancedness results are obtained for relaxations of simple assignment games.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2005-78.
Date of creation: 2005
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assignment situations; matchings; assignment games; balancedness;
Other versions of this item:
- 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.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
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- 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.
- T. E. S. Raghavan & Tamás Solymosi, 2001. "Assignment games with stable core," International Journal of Game Theory, Springer, vol. 30(2), pages 177-185.
- Quint, Thomas, 1991. "Characterization of Cores of Assignment Games," International Journal of Game Theory, Springer, vol. 19(4), pages 413-20.
- 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.
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