Auctions, Matching and the Law of Aggregate Demand

We develop a model of matching with contracts which incorporates, as special cases, the college admissions problem, the Kelso-Crawford labor market matching model, and ascending package auctions. We introduce a new “law of aggregate demand” for the case of discrete heterogeneous workers and show that, when workers are substitutes, the law is satisfied by the demands of profit maximizing firms. When workers are substitutes and the law is satisfied, truthful reporting is a dominant strategy for workers in a worker-offering auction/matching algorithm. We also parameterize a large class of preferences satisfying the two conditions.

[1]  David Gale,et al.  Stable schedule matching under revealed preference , 2003, J. Econ. Theory.

[2]  U. Rothblum,et al.  Vacancy Chains and Equilibration in Senior-Level Labor Markets , 1997 .

[3]  David Porter,et al.  Combinatorial auction design , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[4]  F. Echenique,et al.  Core many-to-one matchings by fixed-point methods , 2004 .

[5]  A. Roth,et al.  The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design , 1999, The American economic review.

[6]  Atila Abdulkadiroglu,et al.  School Choice: A Mechanism Design Approach , 2003 .

[7]  A. Roth.  Stability and Polarization of Interests in Job Matching , 1984 .

[8]  Paul Milgrom,et al.  Putting Auction Theory to Work , 2004 .

[9]  L. Shapley,et al.  College Admissions and the Stability of Marriage , 1962 .

[10]  Alvin E. Roth,et al.  The Economics of Matching: Stability and Incentives , 1982, Math. Oper. Res..

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

[12]  J. Potters,et al.  Verifying gross substitutability , 2002 .

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

[14]  Parag A. Pathak,et al.  The New York City High School Match , 2005 .

[15]  Yoav Shoham,et al.  Combinatorial Auctions , 2005, Encyclopedia of Wireless Networks.

[16]  A. Roth,et al.  Two-sided matching , 1990 .

[17]  David A. Freedman,et al.  Machiavelli and the Gale-Shapley Algorithm , 1981 .

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

[19]  Hiroyuki Adachi.  On a characterization of stable matchings , 2000 .

[20]  C. Plott,et al.  A BINARY CONFLICT ASCENDING PRICE (BICAP) MECHANISM FOR THE DECENTRALIZED ALLOCATION OF THE RIGHT TO USE RAILROAD TRACKS. , 1996 .

[21]  Jeremy I. Bulow,et al.  Matching and Price Competition , 2003 .

[22]  Paul R. Milgrom,et al.  Putting Auction Theory to Work: The Simultaneous Ascending Auction , 1999, Journal of Political Economy.

[23]  A. Roth.  A natural experiment in the organization of entry-level labor markets: regional markets for new physicians and surgeons in the United Kingdom. , 1991, The American economic review.

[24]  Faruk Gul,et al.  WALRASIAN EQUILIBRIUM WITH GROSS SUBSTITUTES , 1999 .

[25]  A. Sen,et al.  Collective Choice and Social Welfare , 2017 .

[26]  Lawrence M. Ausubel,et al.  The Clock-Proxy Auction: A Practical Combinatorial Auction Design , 2004 .

[27]  Lloyd S. Shapley,et al.  Complements and substitutes in the opttmal assignment problem , 1962 .

[28]  Tamás Fleiner,et al.  A Fixed-Point Approach to Stable Matchings and Some Applications , 2003, Math. Oper. Res..

[29]  Lawrence M. Ausubel,et al.  Ascending Auctions with Package Bidding , 2002 .

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

[31]  Alvin E. Roth,et al.  Conflict and Coincidence of Interest in Job Matching: Some New Results and Open Questions , 1985, Math. Oper. Res..

[32]  A. Roth.  On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets , 1986 .

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

[34]  Atila Abdulkadiroglu,et al.  College admissions with affirmative action , 2005, Int. J. Game Theory.

[35]  Jordi Massó,et al.  Single Agents and the Set of Many-to-One Stable Matchings , 2000, J. Econ. Theory.