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A Simple Selling and Buying Procedure

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  • Perez-Castrillo, David
  • Sotomayor, Marilda

Abstract

For the assignment game, we analyze the following mechanism: sellers, simultaneously, fix their prices first; then buyers, sequentially, decide which object to buy, if any, among the remaining objects. The first phase of the game determines the potential prices, while the second phase determines the actual matching. We prove that the set of subgame perfect equilibria in pure strategies in the strong sense of the mechanism coincides with the set of sellers' optimal stable outcomes when buyers use maximal strategies. That is, the mechanism leads to the maximum equilibrium prices and to an optimal matching.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 103 (2002)
Issue (Month): 2 (April)
Pages: 461-474

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Handle: RePEc:eee:jetheo:v:103:y:2002:i:2:p:461-474

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Web page: http://www.elsevier.com/locate/inca/622869

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References

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  1. Peraz-Castrillo, J., 1992. "Cooperative Outcomes Through Non-Cooperative Games," UFAE and IAE Working Papers 165.92, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-50, March.
  3. José Alcalde Pérez & Antonio Romero-Medina, 1996. "Simple mechanisms to implement the core of college admissions problems," Working Papers. Serie AD 1996-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  4. Perry, M. & Rany, P., 1992. "A Non-Cooperative View of Coalition Formation and the Core," UWO Department of Economics Working Papers 9203, University of Western Ontario, Department of Economics.
  5. José Alcalde, 1995. "Implementation of Stable Solutions to Marriage Problems," Working Papers. Serie AD 1995-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  6. Kamecke, U, 1989. "Non-cooperative Matching Games," International Journal of Game Theory, Springer, vol. 18(4), pages 423-31.
  7. José Alcalde Pérez & Antonio Romero-Medina & David Pérez-Castrillo, 1997. "Hiring procedures to implement stable allocations," Working Papers. Serie AD 1997-10, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  8. Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
  9. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-72, August.
  10. Serrano Roberto, 1995. "A Market to Implement the Core," Journal of Economic Theory, Elsevier, vol. 67(1), pages 285-294, October.
  11. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-88, July.
  12. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
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Citations

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Cited by:
  1. Eduard Alonso-Paulí & David Pérez-Castrillo, 2012. "Codes of Best Practice in competitive markets for managers," Economic Theory, Springer, vol. 49(1), pages 113-141, January.
  2. F. Javier Martinez de Albeniz & Carles Rafels, 2012. "Monge assignment games," Working Papers in Economics 282, Universitat de Barcelona. Espai de Recerca en Economia.
  3. 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.
  4. Ivan Arribas & Amparo Urbano, 2003. "Nash Equilibria In A Model Of Multiproduct Price Competition: An Assignment Problem," Working Papers. Serie AD 2003-21, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  5. Marilda Sotomayor, 2009. "Adjusting prices in the multiple-partners assignment game," International Journal of Game Theory, Springer, vol. 38(4), pages 575-600, November.
  6. Dam Kaniska & Perez-Castrillo David, 2006. "The Principal-Agent Matching Market," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 2(1), pages 1-34, August.
  7. Ahmet Alkan & Alparslan Tuncay, 2014. "Pairing Games and Markets," Working Papers 2014.48, Fondazione Eni Enrico Mattei.
  8. Takashi Hayashi & Toyotaka Sakai, 2009. "Nash implementation of competitive equilibria in the job-matching market," International Journal of Game Theory, Springer, vol. 38(4), pages 453-467, November.
  9. Camina, Ester, 2006. "A generalized assignment game," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 152-161, September.
  10. Sotomayor, Marilda, 2004. "Implementation in the many-to-many matching market," Games and Economic Behavior, Elsevier, vol. 46(1), pages 199-212, January.
  11. Francis Bloch & Effrosyni Diamantoudi, 2011. "Noncooperative formation of coalitions in hedonic games," International Journal of Game Theory, Springer, vol. 40(2), pages 263-280, May.

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