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A Simple Selling and Buying Procedure

Author

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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    2. 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.
    3. Núñez, Marina & Rafels, Carlos & Robles, Francisco, 2020. "A mechanism for package allocation problems with gross substitutes," Journal of Mathematical Economics, Elsevier, vol. 87(C), pages 6-14.
    4. 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.
    5. 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.
    6. Dolgopolov, Arthur & Houser, Daniel & Martinelli, Cesar & Stratmann, Thomas, 2024. "Assignment markets: Theory and experiments," European Economic Review, Elsevier, vol. 165(C).
    7. Francisco Robles, 2016. "An implementation of the Vickrey outcome with gross-substitutes," UB School of Economics Working Papers 2016/353, University of Barcelona School of Economics.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Francisco Robles & Marina Núñez, 2014. "One-seller assignment markets with multiunit demands," UB School of Economics Working Papers 2014/316, University of Barcelona School of Economics.
    13. F. Javier Martinez de Albeniz & Carles Rafels, 2012. "Monge assignment games," Working Papers in Economics 282, Universitat de Barcelona. Espai de Recerca en Economia.
    14. 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.
    15. 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.
    16. Sotomayor, Marilda, 2004. "Implementation in the many-to-many matching market," Games and Economic Behavior, Elsevier, vol. 46(1), pages 199-212, January.
    17. Camina, Ester, 2006. "A generalized assignment game," Mathematical Social Sciences, Elsevier, vol. 52(2), pages 152-161, September.
    18. Ahmet Alkan & Alparslan Tuncay, 2014. "Pairing Games and Markets," Working Papers 2014.48, Fondazione Eni Enrico Mattei.
    19. Pérez-Castrillo, David & Sotomayor, Marilda, 2003. "A Selling Mechanism," Revista Brasileira de Economia - RBE, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil), vol. 57(4), October.
    20. 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.

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    Keywords

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    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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