International Journal of Game Theory

, Volume 46, Issue 4, pp 1137–1161 | Cite as

On the manipulability of competitive equilibrium rules in many-to-many buyer–seller markets

  • David Pérez-CastrilloEmail author
  • Marilda Sotomayor
Original Paper


We analyze the manipulability of competitive equilibrium allocation rules for the simplest many-to-many extension of Shapley and Shubik’s (Int J Game Theory 1:111–130, 1972) assignment game. First, we show that if an agent has a quota of one, then she does not have an incentive to manipulate any competitive equilibrium rule that gives her her most preferred competitive equilibrium payoff when she reports truthfully. In particular, this result extends to the one-to-many (respectively, many-to-one) models the Non-Manipulability Theorem of the buyers (respectively, sellers), proven by Demange (Strategyproofness in the assignment market game. École Polytechnique, Laboratoire d’Économetrie, Paris, 1982), Leonard (J Polit Econ 91:461–479, 1983), and Demange and Gale (Econometrica 55:873–888, 1985) for the assignment game. Second, we prove a “General Manipulability Theorem” that implies and generalizes two “folk theorems” for the assignment game, the Manipulability Theorem and the General Impossibility Theorem, never proven before. For the one-to-one case, this result provides a sort of converse of the Non-Manipulability Theorem.


Matching Competitive equilibrium Optimal competitive equilibrium Manipulability Competitive equilibrium rule 


C78 D78 


  1. Andersson T, Ehlers L, Svensson LG (2014) Budget balance, fairness, and minimal manipulability. Theor Econ 9:753–777CrossRefGoogle Scholar
  2. Andersson T, Svensson LG (2008) Non-manipulable assignment of individuals to positions revisited. Math Soc Sci 56:350–354CrossRefGoogle Scholar
  3. Ausubel L (2004) An efficient ascending-bid auction for multiple objects. Am Econ Rev 94:1452–1475CrossRefGoogle Scholar
  4. Ausubel L (2006) An efficient dynamic auction for heterogeneous commodities. Am Econ Rev 96:602–629CrossRefGoogle Scholar
  5. Barberà S, Berga D, Moreno B (2016) Group strategy-proofness in private good economies. Am Econ Rev 106:1073–1099CrossRefGoogle Scholar
  6. Crawford VP, Knoer EM (1981) Job matching with heterogeneous firms and workers. Econometrica 49:437–450CrossRefGoogle Scholar
  7. Demange G (1982) Strategyproofness in the assignment market game. École Polytechnique, Laboratoire d’Économetrie, Paris (Preprint) Google Scholar
  8. Demange G, Gale D (1985) The strategy structure of two-sided matching markets. Econometrica 55:873–888CrossRefGoogle Scholar
  9. Demange G, Gale D, Sotomayor M (1986) Multi-item auctions. J Polit Econ 94:863–872CrossRefGoogle Scholar
  10. Fujinaka Y, Wakayama T (2015) Maximal manipulation of envy-free solutions in economies with indivisible goods and money. J Econ Theory 158:165–185CrossRefGoogle Scholar
  11. Gale D (1960) The theory of linear economic models. McGraw Hill, New YorkGoogle Scholar
  12. Gul F, Stacchetti E (2000) The English auction with differential commodities. J Econ Theory 92:66–95CrossRefGoogle Scholar
  13. Hatfield JW, Milgrom PR (2005) Matching with contracts. Am Econ Rev 95:913–935CrossRefGoogle Scholar
  14. Jaramillo P, Kayi C, Klijn F (2013) Equilibria under deferred acceptance: dropping strategies, filled positions, and welfare. Game Econ Behav 82:693–701CrossRefGoogle Scholar
  15. Jaume D, Massó J, Neme A (2012) The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria. Math Methods Oper Res 76:161–187CrossRefGoogle Scholar
  16. Kelso A, Crawford VP (1982) Job matching, coalition formation, and gross substitutes. Econometrica 50:1483–1504CrossRefGoogle Scholar
  17. Kojima F, Pathak PA (2009) Incentives and stability in large two-sided matching markets. Am Econ Rev 99:608–627CrossRefGoogle Scholar
  18. Leonard HB (1983) Elicitation of honest preferences for the assignment of individuals to positions. J Polit Econ 91:461–479CrossRefGoogle Scholar
  19. Ma J (2010) The singleton core in the hospital-admissions problem and its application to the National Resident Matching Program (NRMP). Game Econ Behav 69:150–164CrossRefGoogle Scholar
  20. Miyake M (1998) On the incentive properties of multi-item auctions. Int J Game Theory 27:1–19CrossRefGoogle Scholar
  21. Roth A (1985) The college admissions problem is not equivalent to the marriage problem. J Econ Theory 36:277–288CrossRefGoogle Scholar
  22. Roth A, Sotomayor M (1990) Two-sided matching. A study in game-theoretic modeling and analysis. Econometric society monograph series, vol 18. Cambridge University Press, New YorkGoogle Scholar
  23. Sakai T (2011) A note on strategy-proofness from the doctor side in matching with contracts. Rev Econ Des 15:337–342Google Scholar
  24. Shapley L, Shubik M (1972) The assignment game I: the core. Int J Game Theory 1:111–130CrossRefGoogle Scholar
  25. Sotomayor M (1992) The multiple partners game. In: Majumdar M (ed) Equilibrium and dynamics. The MacMillan Press LTD, LondonGoogle Scholar
  26. Sotomayor M (1999) The lattice structure of the set of stable outcomes of the multiple partners assignment game. Int J Game Theory 28:567–583CrossRefGoogle Scholar
  27. Sotomayor M (2000) Buying and selling mechanisms with random matching rules yielding pricing competition. (Unpublished WP)Google Scholar
  28. Sotomayor M (2003) Some further remark on the core structure of the assignment game. J Econ Theory 46:261–265Google Scholar
  29. Sotomayor M (2007) Connecting the cooperative and competitive structures of the multiple-partners assignment game. J Econ Theory 134:155–174CrossRefGoogle Scholar
  30. Sotomayor M (2008) Labor time shared in the assignment game lending new insights to the theory of two-sided matching markets. First version, 2008 (pre-print in FEA/USP WPA 2012-29)Google Scholar
  31. Sotomayor M (2012) A further note on the college admission game. Int J Game Theory 41:179–193CrossRefGoogle Scholar
  32. Sun N, Yang Z (2003) A general strategy proof fair allocation mechanism. Econ Lett 81:73–79CrossRefGoogle Scholar
  33. Sun N, Yang Z (2014) An efficient and incentive compatible dynamic auction for multiple complements. J Polit Econ 122:422–466CrossRefGoogle Scholar
  34. Svensson LG (2009) Coalitional strategy-proofness and fairness. Econ Theory 40:227–245CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Dept. Economía e Hist. Económica, Edificio BUniversitat Autònoma de Barcelona and Barcelona GSEBarcelonaSpain
  2. 2.Dep de EconomiaUniversidade de São Paulo-SPSão PauloBrazil
  3. 3.Graduate School of EconomicsGetulio Vargas Foundation-RJRio de JaneiroBrazil

Personalised recommendations