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

Author

Listed:
  • 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.

Suggested Citation

  • Marilda Sotomayor, 1999. "The lattice structure of the set of stable outcomes of the multiple partners assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 567-583.
  • 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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    Cited by:

    1. repec:sbe:breart:v:25:y:2005:i:2:a:2506 is not listed on IDEAS
    2. Sotomayor, Marilda, 2002. "A Simultaneous Descending Bid Auction for Multiple Items and Unitary Demand," Revista Brasileira de Economia - RBE, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 56(3), July.
    3. Paula Jaramillo & Çaǧatay Kayı & Flip Klijn, 2014. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 793-811, April.
    4. Daniel Jaume & Jordi Massó & Alejandro Neme, 2012. "The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(2), pages 161-187, October.
    5. 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.
    6. Jeremy T. Fox, 2010. "Identification in matching games," Quantitative Economics, Econometric Society, vol. 1(2), pages 203-254, November.
    7. Friedel Bolle & Philipp E. Otto, 2016. "Role-dependent Social Preferences," Economica, London School of Economics and Political Science, vol. 83(332), pages 704-740, October.
    8. Jeremy T. Fox & David H. Hsu & Chenyu Yang, 2012. "Unobserved Heterogeneity in Matching Games with an Application to Venture Capital," NBER Working Papers 18168, National Bureau of Economic Research, Inc.
    9. Jeremy T. Fox, 2008. "Estimating Matching Games with Transfers," NBER Working Papers 14382, National Bureau of Economic Research, Inc.
    10. Peter Biro & Walter Kern & Daniel Paulusma & Peter Wojuteczky, 2015. "The Stable Fixtures Problem with Payments," IEHAS Discussion Papers 1545, Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences.
    11. 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.
    12. repec:spr:compst:v:76:y:2012:i:2:p:161-187 is not listed on IDEAS
    13. Nikhil Agarwal, 2015. "An Empirical Model of the Medical Match," American Economic Review, American Economic Association, vol. 105(7), pages 1939-1978, July.
    14. Camina, Ester, 2006. "A generalized assignment game," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 152-161, September.
    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. Emiliya Lazarova & Peter Borm & Arantza Estévez-Fernández, 2016. "Transfers and exchange-stability in two-sided matching problems," Theory and Decision, Springer, vol. 81(1), pages 53-71, June.
    17. repec:spr:jogath:v:46:y:2017:i:4:d:10.1007_s00182-017-0573-y is not listed on IDEAS
    18. 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.
    19. Andersson, Tommy, 2007. "An algorithm for identifying fair and optimal allocations," Economics Letters, Elsevier, vol. 96(3), pages 337-342, September.
    20. Massó, Jordi & Neme, Alejandro, 2014. "On cooperative solutions of a generalized assignment game: Limit theorems to the set of competitive equilibria," Journal of Economic Theory, Elsevier, vol. 154(C), pages 187-215.
    21. Sotomayor, Marilda, 2007. "Connecting the cooperative and competitive structures of the multiple-partners assignment game," Journal of Economic Theory, Elsevier, vol. 134(1), pages 155-174, May.
    22. 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.
    23. Pérez-Castrillo, David & Sotomayor, Marilda, 2003. "A Selling Mechanism," Revista Brasileira de Economia - RBE, FGV/EPGE - Escola Brasileira de Economia e Finanças, Getulio Vargas Foundation (Brazil), vol. 57(4), October.
    24. 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).
    25. Ruth Mart?ez & Jordi MassóAuthor-Name: Alejandro Neme & Jorge Oviedo, "undated". "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).

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