On the manipulability of competitive equilibrium rules in many-to-many buyer-seller markets
Pérez-Castrillo, David (Universitat Autònoma de Barcelona. Departament d'Economia i d'Història Econòmica)
Sotomayor, Marilda A. Oliveira (Universidade de São Paulo)

Date:	2017
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.
Grants:	Ministerio de Economía y Competitividad ECO2012-31962 Ministerio de Economía y Competitividad EECO2015-63679-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014SGR-142 Ministerio de Economía y Competitividad SEV-2015-0563
Note:	We thank participants of seminars at the Universities of Salamanca, Valencia, Osaka, Waseda, East Anglia, and Seoul National, at the workshop on Game Theory in Rio de Janeiro, MOVE-Jerusalem, and ASSET meeting in Aix Marseille, as well as two reviewers and an Associate Editor for very helpful comments for very helpful comments. Marilda Sotomayor acknowledges financial support from CNPq-Brazil. David Pérez-Castrillo is a fellow of MOVE. He acknowledges financial support from the Ministerio de Ciencia y Tecnología (ECO2012-31962 and 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. Previous versions of this paper, analyzing one-to-one matching models only, circulated under the titles "Two Folk Manipulability Theorems in One-to-one Two-sided Matching Markets with Money as a Continuous Variable" and "Two Folk Manipulability Theorems in the General One-to-one Two-sided Matching Markets with Money".
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Matching ; Competitive equilibrium ; Optimal competitive equilibrium ; Manipulability ; Competitive equilibrium rule
Published in:	International journal of game theory, 2017, p. 1-25, ISSN 0020-7276

DOI: 10.1007/s00182-017-0573-y

Postprint 30 p, 322.3 KB

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