A Unifying Model for Matching Situations
AbstractAbstract: We present a unifying framework for transferable utility coalitional games that are derived from a non-negative matrix in which every entry represents the value obtained by combining the corresponding row and column. We assume that every row and every column is associated with a player, and that every player is associated with at most one row and at most one column. The instances arising from this framework are called matching games, and they encompass assignment games and permutation games as two polar cases. We show that the core of a matching game is always nonempty by proving that the set of matching games coincides with the set of permutation games. Then we focus on two separate problems. First, we exploit the wide range of situations comprised in our framework to investigate the relationship between matching games with different player sets but defined by the same underlying matrix. We show that the core is not only immune to the merging of a row player and a column player, but also to the reverse manipulation, i.e., to the splitting of a player into a row player and a column player. Other common solution concepts fail to be either merging-proof or splitting-proof in general. Second, we focus on permutation games only and we analyze the set of all matrices that define permutation games with the same core. In contrast to assignment games, we show that there can be multiple matrices whose entries cannot be raised without modifying the core of the corresponding permutation game and that, for small instances, every such matrix defines an exact game.
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Bibliographic InfoPaper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number 2013-069.
Date of creation: 2013
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Web page: http://center.uvt.nl
matching situations; permutation games; assignment games;
Find related papers by JEL classification:
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-12-29 (All new papers)
- NEP-GTH-2013-12-29 (Game Theory)
- NEP-UPT-2013-12-29 (Utility Models & Prospect Theory)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Quint, Thomas, 1996. "On One-Sided versus Two-Sided Matching Games," Games and Economic Behavior, Elsevier, vol. 16(1), pages 124-134, September.
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- O. Tejada and M. Alvarez-Mozos, 2012. "Vertical Syndication-Proof Competitive Prices in Multilateral Markets," Working Papers in Economics 283, Universitat de Barcelona. Espai de Recerca en Economia.
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- Martínez-de-Albéniz, F. Javier & Núñez, Marina & Rafels, Carles, 2011.
"Assignment markets with the same core,"
Games and Economic Behavior,
Elsevier, vol. 73(2), pages 553-563.
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