Assignment Exchanges

We analyze "assignment exchanges"- auction and exchange mechanisms which are tight simplifications of direct Walrasian exchange mechanisms. These simplifications are distinguished by their use of assignment messages, which parameterize certain substitutable preferences. The "basic" assignment exchanges respect integer constraints, generalizing the Shapley-Shubik mechanism for indivisible goods. Connections are reported between the assignment exchanges, ascending multi-product clock auctions, uniform price auctions for a single product, and Vickrey auctions. The exchange mechanisms accommodate bids by buyers, sellers and swappers and can support trading for certain kinds of complementary goods.

[1]  Kjell G. Nyborg,et al.  Divisible-Good Auctions: The Role of Allocation Rules , 2004 .

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

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

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

[5]  Vincent P. Crawford,et al.  The Flexible-Salary Match: A Proposal to Increase the Salary Flexibility of the National Resident Matching Program , 2005 .

[6]  Craig Boutilier,et al.  Bidding Languages for Combinatorial Auctions , 2001, IJCAI.

[7]  P. Jehiel.  On the virtues of the ascending price auction : New insights in the private value setting , 2000 .

[8]  David C. Parkes,et al.  Auction design with costly preference elicitation , 2005, Annals of Mathematics and Artificial Intelligence.

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

[10]  Noam Nisan,et al.  The communication requirements of efficient allocations and supporting prices , 2006, J. Econ. Theory.

[11]  Robert B. Wilson.  Auctions of Shares , 1979 .

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

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

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

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

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

[17]  Paul R. Milgrom,et al.  Package Auctions and Package Exchanges , 2005 .

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

[19]  Michel Gendreau,et al.  Combinatorial auctions , 2007, Ann. Oper. Res..

[20]  Paul Milgrom,et al.  Substitute goods, auctions, and equilibrium , 2009, J. Econ. Theory.

[21]  Donald M. Topkis,et al.  Minimizing a Submodular Function on a Lattice , 1978, Oper. Res..

[22]  Paul Milgrom,et al.  Simplified Mechanisms with Applications to Sponsored Search and Package Auctions , 2007 .