Economic Theory

, Volume 64, Issue 1, pp 99–119 | Cite as

The outcome of competitive equilibrium rules in buyer–seller markets when the agents play strategically

  • David Pérez-CastrilloEmail author
  • Marilda Sotomayor
Research Article


We analyze the two-stage games induced by competitive equilibrium rules for the buyer–seller market of Shapley and Shubik (Int J Game Theory 1:111–130, 1972). In these procedures, first sellers and then buyers report their valuation and the outcome is determined by a competitive equilibrium outcome for the market reported by the agents. We provide results concerning buyers and sellers’ equilibrium strategies. In particular, our results point out that, by playing first, sellers are able to instigate an outcome that corresponds to the sellers’ optimal competitive equilibrium allocation for the true market.


Assignment game Competitive price Optimal matching Competitive rule 

JEL Classification

C78 D78 



We thank three reviewers and an Associate Editor for very helpful comments. Marilda Sotomayor is a research fellow at CNPq-Brazil. David Pérez-Castrillo is a fellow of MOVE and CESIfo. He acknowledges financial support from the Ministerio de Ciencia y Tecnología (ECO2015-63679-P), Generalitat de Catalunya (2014SGR-142), the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2015-0563) and ICREA Academia.


  1. Alcalde, J., Pérez-Castrillo, D., Romero-Medina, A.: Hiring procedures to implement stable allocations. J. Econ. Theory 82, 469–480 (1998)CrossRefGoogle Scholar
  2. Budish, E.: The combinatorial assignment problem: approximate competitive equilibrium from equal incomes. J. Polit. Econ. 119, 1061–1103 (2011)CrossRefGoogle Scholar
  3. Demange, G.: Strategyproofness in the assignment market game. Preprint. École Polytechnique, Laboratoire d’Économetrie, Paris (1982)Google Scholar
  4. Demange, G., Gale, D.: The strategy structure of two-sided matching markets. Econometrica 55, 873–88 (1985)CrossRefGoogle Scholar
  5. Gale, D.: The Theory of Linear Economic Models. McGraw Hill, New York (1960)Google Scholar
  6. Gale, D., Sotomayor, M.: Ms. Machiavelli and the stable matching problem. Am. Math. Mon. 92, 261–268 (1985a)Google Scholar
  7. Gale, D., Sotomayor, M.: Some remarks on the stable matching problem. Discret. Appl. Math. 11, 223–232 (1985b)Google Scholar
  8. Hayashi, T., Sakai, T.: Nash implementation of competitive equilibria in the job-matching market. Int. J. Game Theory 38, 453–467 (2009)CrossRefGoogle Scholar
  9. Jaramillo, P., Kayi, C., Klijn, F.: Equilibria under deferred acceptance: dropping strategies, filled positions, and welfare. Games Econ. Behav. 82, 693–701 (2013)CrossRefGoogle Scholar
  10. Kamecke, U.: Non-cooperative matching games. Int. J. Game Theory 18, 423–431 (1989)CrossRefGoogle Scholar
  11. Kelso, A., Crawford, V.P.: Job matching, coalition formation, and gross substitutes. Econometrica 50, 1483–1504 (1982)CrossRefGoogle Scholar
  12. Kojima, F., Pathak, P.A.: Incentives and stability in large two-sided matching markets. Am. Econ. Rev. 99, 608–627 (2009)CrossRefGoogle Scholar
  13. Leonard, H.B.: Elicitation of honest preferences for the assignment of individuals to positions. J. Polit. Econ. 91, 461–479 (1983)CrossRefGoogle Scholar
  14. Ma, J.: The singleton core in the hospital-admissions problem and its application to the National Resident Matching Program (NRMP). Games Econ. Behav. 69, 150–164 (2010)CrossRefGoogle Scholar
  15. Pérez-Castrillo, D., Sotomayor, M.: A simple selling and buying procedure. J. Econ. Theory 103, 461–474 (2002)CrossRefGoogle Scholar
  16. Pérez-Castrillo, D., Sotomayor, M.: On the manipulability of competitive equilibrium rules in many-to-many buyer–seller markets. W.P, BGSE (2013)Google Scholar
  17. Roth, A.: The college admissions problem is not equivalent to the marriage problem. J. Econ. Theory 36, 277–288 (1985)CrossRefGoogle Scholar
  18. Roth, A., Sotomayor, M.: Two-sided matching. A study in game-theoretic modeling and analysis. Econometric Society Monograph Series, vol. 18, Cambridge University Press, Cambridge (1990)Google Scholar
  19. Shapley, L., Shubik, M.: The assignment game I: the core. Int. J. Game Theory 1, 111–130 (1972)CrossRefGoogle Scholar
  20. Sotomayor, M.: On incentives in a two-sided matching market. Pontificia Universidade Católica do Rio de Janeiro, W.P. Department of Mathematics (1986)Google Scholar
  21. Sotomayor, M.: Existence of stable outcomes and the lattice property for a unified matching market. Math. Soc. Sci. 39, 119–132 (2000)CrossRefGoogle Scholar
  22. Sotomayor, M.: A simultaneous descending bid auction for multiple items and unitary demand. Rev. Bras. Econ. 56, 497–510 (2002)CrossRefGoogle Scholar
  23. Sotomayor, M.: Connecting the cooperative and competitive structures of the multiple-partners assignment game. J. Econ. Theory 134, 155–74 (2007)CrossRefGoogle Scholar
  24. Sotomayor, M.: Admission games induced by stable matching rules. Int. J. Game Theory 36, 621–640 (2008)CrossRefGoogle Scholar
  25. Sotomayor, M.: A further note on the college admission game. Int. J. Game Theory 41, 179–193 (2012)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Dept. Economía e Hist. EconómicaUniversitat Autònoma de Barcelona and Barcelona GSEBellaterraSpain
  2. 2.Dep de EconomiaUniversity of São PauloSão PauloBrazil

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