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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

Abstract

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.

Keywords

Matching Competitive equilibrium Optimal competitive equilibrium Manipulability Competitive equilibrium rule 

JEL

C78 D78 

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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

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