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A Simple Selling and Buying Procedure

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Abstract

For the assignment game, we anlayze 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 proces, 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.

Suggested Citation

  • Perez-Castrillo, D. & Sotomayor, M., 1998. "A Simple Selling and Buying Procedure," UFAE and IAE Working Papers 421.98, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  • Handle: RePEc:aub:autbar:421.98
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    References listed on IDEAS

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    1. Perry, Motty & Reny, Philip J, 1994. "A Noncooperative View of Coalition Formation and the Core," Econometrica, Econometric Society, vol. 62(4), pages 795-817, July.
    2. Alcalde, Jose, 1996. "Implementation of Stable Solutions to Marriage Problems," Journal of Economic Theory, Elsevier, vol. 69(1), pages 240-254, April.
    3. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882.
    4. Perez-Castrillo J. David, 1994. "Cooperative Outcomes through Noncooperative Games," Games and Economic Behavior, Elsevier, vol. 7(3), pages 428-440, November.
    5. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
    6. Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
    7. Serrano Roberto, 1995. "A Market to Implement the Core," Journal of Economic Theory, Elsevier, vol. 67(1), pages 285-294, October.
    8. Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
    9. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    10. Alcalde, Jose & Romero-Medina, Antonio, 2000. "Simple Mechanisms to Implement the Core of College Admissions Problems," Games and Economic Behavior, Elsevier, vol. 31(2), pages 294-302, May.
    11. Alcalde, Jose & Perez-Castrillo, David & Romero-Medina, Antonio, 1998. "Hiring Procedures to Implement Stable Allocations," Journal of Economic Theory, Elsevier, vol. 82(2), pages 469-480, October.
    12. Kamecke, U, 1989. "Non-cooperative Matching Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(4), pages 423-431.
    13. 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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    Cited by:

    1. Camina, Ester, 2006. "A generalized assignment game," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 152-161, September.
    2. 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.
    3. repec:spr:joecth:v:64:y:2017:i:1:d:10.1007_s00199-016-0997-9 is not listed on IDEAS
    4. Francisco Robles, 2016. "An implementation of the Vickrey outcome with gross-substitutes," UB Economics Working Papers 2016/353, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.
    5. Ahmet Alkan & Alparslan Tuncay, 2014. "Pairing Games and Markets," Working Papers 2014.48, Fondazione Eni Enrico Mattei.
    6. 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.
    7. Arribas, Ivan & Urbano, Amparo, 2005. "Nash equilibria in a model of multiproduct price competition: an assignment problem," Journal of Mathematical Economics, Elsevier, vol. 41(3), pages 351-385, April.
    8. David Pérez-Castrillo & Marilda Sotomayor, 2017. "The outcome of competitive equilibrium rules in buyer–seller markets when the agents play strategically," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 64(1), pages 99-119, June.
    9. repec:eee:jetheo:v:169:y:2017:i:c:p:425-452 is not listed on IDEAS
    10. 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.
    11. 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.
    12. Eduard Alonso-Paulí & David Pérez-Castrillo, 2012. "Codes of Best Practice in competitive markets for managers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 49(1), pages 113-141, January.
    13. Francis Bloch & Effrosyni Diamantoudi, 2011. "Noncooperative formation of coalitions in hedonic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(2), pages 263-280, May.
    14. Trudeau, Christian & Vidal-Puga, Juan, 2017. "On the set of extreme core allocations for minimal cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 169(C), pages 425-452.
    15. Marilda Sotomayor, 2009. "Adjusting prices in the multiple-partners assignment game," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(4), pages 575-600, November.
    16. Takashi Hayashi & Toyotaka Sakai, 2009. "Nash implementation of competitive equilibria in the job-matching market," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(4), pages 453-467, November.
    17. Francisco Robles & Marina Núñez, 2014. "One-seller assignment markets with multiunit demands," UB Economics Working Papers 2014/316, Universitat de Barcelona, Facultat d'Economia i Empresa, UB Economics.
    18. F. Javier Martinez de Albeniz & Carles Rafels, 2012. "Monge assignment games," Working Papers in Economics 282, Universitat de Barcelona. Espai de Recerca en Economia.
    19. Sotomayor, Marilda, 2004. "Implementation in the many-to-many matching market," Games and Economic Behavior, Elsevier, vol. 46(1), pages 199-212, January.

    More about this item

    Keywords

    MODELS ; GAMES;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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