A geometric chracterization of the nucleolus of the assignment game
AbstractMaschler et al. (1979) provide a geometrical characterization for the intersection of the kernel and the core of a coalitional game, showing that those allocations that lie in both sets are always the midpoint of certain bargaining range between each pair of players. In the case of the assignment game, this means that the kernel can be determined as those core allocations where the maximum amount, that can be transferred without getting outside the core, from one agent to his/her optimally matched partner equals the maximum amount that he/she can receive from this partner, also remaining inside the core (Rochford, 1984). We now prove that the nucleolus of the assignment game can be characterized by requiring this bisection property be satisfied not only for optimally matched pairs but also for optimally matched coalitions.
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Bibliographic InfoPaper provided by Universitat de Barcelona. Espai de Recerca en Economia in its series Working Papers in Economics with number 260.
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Date of creation: 2011
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Other versions of this item:
- Francesc Llerena & Marina Nunez, 2011. "A geometric characterization of the nucleolus of the assignment game," Economics Bulletin, AccessEcon, vol. 31(4), pages 3275-3285.
- 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
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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, Springer, vol. 23(2), pages 119-43.
- F. Javier Martínez-de-Albéniz & Carles Rafels & Neus Ybern, 2013.
"On the nucleolus of 2 x 2 assignment games,"
AccessEcon, vol. 33(2), pages 1641-1648.
- F. Javier Martinez de Albeniz & Carles Rafels & Neus Ybern, 2013. "On the nucleolus of 2 x 2 assignment games," Working Papers in Economics, Universitat de Barcelona. Espai de Recerca en Economia 289, Universitat de Barcelona. Espai de Recerca en Economia.
- 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, Universitat de Barcelona. Espai de Recerca en Economia 286, Universitat de Barcelona. Espai de Recerca en Economia.
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