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

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.

[1]  Lawrence M. Ausubel.  An Efficient Ascending-Bid Auction for Multiple Objects , 2004 .

[2]  L. Shapley,et al.  The assignment game I: The core , 1971 .

[3]  Marilda Sotomayor,et al.  The lattice structure of the set of stable outcomes of the multiple partners assignment game , 1999, Int. J. Game Theory.

[4]  Toyotaka Sakai,et al.  A note on strategy-proofness from the doctor side in matching with contracts , 2011 .

[5]  Ning Sun,et al.  A General Strategy Proof Fair Allocation Mechanism , 2003 .

[6]  Tommy Andersson,et al.  Budget-Balance, Fairness and Minimal Manipulability , 2014 .

[7]  D. Gale,et al.  Multi-Item Auctions , 1986, Journal of Political Economy.

[8]  V. Crawford,et al.  Job Matching, Coalition Formation, and Gross Substitutes , 1982 .

[9]  Ning Sun,et al.  An Efficient and Incentive Compatible Dynamic Auction for Multiple Complements , 2014, Journal of Political Economy.

[10]  Marilda Sotomayor.  A further note on the college admission game , 2012, Int. J. Game Theory.

[11]  Mitsunobu Miyake,et al.  On the incentive properties of multi-item auctions , 1998, Int. J. Game Theory.

[12]  H. Leonard.  Elicitation of Honest Preferences for the Assignment of Individuals to Positions , 1983, Journal of Political Economy.

[13]  Steven Vajda,et al.  The Theory of Linear Economic Models , 1960 .

[14]  Yuji Fujinaka,et al.  Maximal Manipulation of Envy-Free Solutions in Economies with Indivisible Goods and Money , 2015, J. Econ. Theory.

[15]  Jordi Massó,et al.  The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria , 2012, Math. Methods Oper. Res..

[16]  Lars-Gunnar Svensson,et al.  Coalitional strategy-proofness and fairness , 2009 .

[17]  Paul R. Milgrom,et al.  Matching with Contracts , 2005 .

[18]  Ennio Stacchetti,et al.  The English Auction with Differentiated Commodities , 2000, J. Econ. Theory.

[19]  Marilda Sotomayor,et al.  Connecting the cooperative and competitive structures of the multiple-partners assignment game , 2007, J. Econ. Theory.

[20]  Flip Klijn,et al.  Equilibria under deferred acceptance: Dropping strategies, filled positions, and welfare , 2013 .

[21]  Alvin E. Roth,et al.  Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis , 1990 .

[22]  Marilda Sotomayor,et al.  Some further remark on the core structure of the assignment game , 2003, Math. Soc. Sci..

[23]  Lawrence M. Ausubel.  An efficient dynamic auction for heterogeneous commodities , 2006 .

[24]  Alvin E. Roth,et al.  Stable Outcomes in Discrete and Continuous Models of Two-Sided Matching: a Unified Treatment , 1996 .

[25]  V. Crawford,et al.  Job Matching with Heterogeneous Firms and Workers , 1981 .

[26]  D. Gale,et al.  The Strategy Structure of Two Sided Matching Markets , 1985 .

[27]  Marilda Sotomayor,et al.  The Multiple Partners Game , 1992 .

[28]  Jinpeng Ma,et al.  The singleton core in the college admissions problem and its application to the National Resident Matching Program (NRMP) , 2010, Games Econ. Behav..

[29]  Parag A. Pathak,et al.  Appendix to "Incentives and Stability in Large Two-Sided Matching Markets" , 2009 .

[30]  A. Roth.  The college admissions problem is not equivalent to the marriage problem , 1985 .

[31]  S. Barberà,et al.  Group Strategy-Proofness in Private Good Economies , 2014 .

[32]  Tommy Andersson,et al.  Non-manipulable assignment of individuals to positions revisited , 2008, Math. Soc. Sci..