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The lattice structure of the set of stable outcomes of the multiple partners assignment game

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  • Marilda Sotomayor

    ()
    (Department of Economics, Universidade de Sao Paulo, Av. Prof. Luciano Gualberto 908, Cidade Universitaria, Sao Paulo - 05508-900, Brazil)

Abstract

The Multiple Partners assignment game is a natural extension of the Shapley and Shubik Assignment Game (Shapley and Shubik, 1972) to the case where the participants can form more than one partnership. In Sotomayor (1992) the existence of stable outcomes was proved. For the sake of completeness the proof is reproduced in Appendix I. In this paper we show that, as in the Assignment Game, stable payoffs form a complete lattice and hence there exists a unique optimal stable payoff for each side of the market. We also observe a polarization of interests between the two sides of the matching, within the whole set of stable payoffs. Our proofs differ technically from the Shapley and Shubik's proofs since they depend on a central result (Theorem 1) which has no parallel in the Assignment model.

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 28 (1999)
Issue (Month): 4 ()
Pages: 567-583

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Handle: RePEc:spr:jogath:v:28:y:1999:i:4:p:567-583

Note: Received: June 1996/Revised version: February 1999
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Web page: http://link.springer.de/link/service/journals/00182/index.htm

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Related research

Keywords: Matching · lattice · optimal matching · optimal stable outcomes;

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Citations

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Cited by:
  1. Ester Cami?, 2002. "A Generalized Assignment Game," UFAE and IAE Working Papers 514.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Daniel Jaume & Jordi Massó & Alejandro Neme, 2010. "The Multiple-partners Assignment Game with Heterogeneous Sales and Multi-unit Demands: Competitive Equilibria," UFAE and IAE Working Papers 808.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  3. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.
  4. Pablo Arribillaga & Jordi Massó & Alejandro Neme, 2013. "On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game," Working Papers 740, Barcelona Graduate School of Economics.
  5. Andersson, Tommy, 2007. "An algorithm for identifying fair and optimal allocations," Economics Letters, Elsevier, vol. 96(3), pages 337-342, September.
  6. Marina Nunez Oliva & Carlos Rafels Pallarola, 2001. "The extreme core allocations of the assignment game," Working Papers in Economics 65, Universitat de Barcelona. Espai de Recerca en Economia.
  7. Daniel Jaume & Jordi Massó & Alejandro Neme, 2012. "The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria," Computational Statistics, Springer, vol. 76(2), pages 161-187, October.
  8. Paula Jaramillo & Çagatay Kayi & Flip Klijn, 2012. "On the Exhaustiveness of Truncation and Dropping Strategies in Many-to-Many Matching Markets," Working Papers 632, Barcelona Graduate School of Economics.
  9. Fagebaume, Alexis & Gale, David & Sotomayor, Marilda, 2010. "A note on the multiple partners assignment game," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 388-392, July.
  10. Jordi Massó & Alejandro Neme, 2010. "On Cooperative Solutions of a Generalized Assignment Game: Limit Theorems to the Set of Competitive Equilibria," UFAE and IAE Working Papers 810.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  11. Martinez, Ruth & Masso, Jordi & Neme, Alejandro & Oviedo, Jorge, 2004. "An algorithm to compute the full set of many-to-many stable matchings," Mathematical Social Sciences, Elsevier, vol. 47(2), pages 187-210, March.
  12. Bolle, Friedel & Breitmoser, Yves & Otto, Philipp E., 2011. "A positive theory of cooperative games: The logit core and its variants," MPRA Paper 32918, University Library of Munich, Germany.
  13. Ruth Mart?ez & Jordi MassóAuthor-Name: Alejandro Neme & Jorge Oviedo, . "An Algorithm To Compute The Set Of Many-To-Many Stable Matchings," UFAE and IAE Working Papers 457.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  14. R. Pablo Arribillaga & Jordi Massó & Alejandro Neme, 2013. "On the Structure of Cooperative and Competitive Solutions for a Generalized Assignment Game," UFAE and IAE Working Papers 940.13, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  15. Kucuksenel, Serkan, 2011. "Core of the assignment game via fixed point methods," Journal of Mathematical Economics, Elsevier, vol. 47(1), pages 72-76, January.
  16. Jeremy T. Fox, 2008. "Estimating Matching Games with Transfers," NBER Working Papers 14382, National Bureau of Economic Research, Inc.

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