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An Auction with Approximated Bidder Preferences - When an Auction has to be Quick

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Abstract

This paper presents a combinatorial auction which is of particular interest when short completion times are of importance. It is based on a method for approximating the bidders' preferences over two types of items when complementarity between the two may exist. The resulting approximated preference relation is shown to be complete and transitive at any given price vector. It is shown that an approximated Walrasian equilibrium always exists if the approximated preferences of the bidders comply with the gross substitutes condition. This condition also ensures that the set of approximated equilibrium prices forms a complete lattice. A process is proposed which is shown to always reach the smallest approximated Walrasian price vector.

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  • Ingebretsen Carlson, Jim, 2016. "An Auction with Approximated Bidder Preferences - When an Auction has to be Quick," Working Papers 2016:12, Lund University, Department of Economics.
    • Handle: RePEc:hhs:lunewp:2016_012
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    1. T. Andersson & C. Andersson & A. Talman, 2013. "Sets in excess demand in simple ascending auctions with unit-demand bidders," Annals of Operations Research, Springer, vol. 211(1), pages 27-36, December.
    2. Demange, Gabrielle & Gale, David, 1985. "The Strategy Structure of Two-sided Matching Markets," Econometrica, Econometric Society, vol. 53(4), pages 873-888, July.
    3. Ken Binmore & Paul Klemperer, 2002. "The Biggest Auction Ever: the Sale of the British 3G Telecom Licences," Economic Journal, Royal Economic Society, vol. 112(478), pages 74-96, March.
    4. Ausubel Lawrence M & Milgrom Paul R, 2002. "Ascending Auctions with Package Bidding," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 1(1), pages 1-44, August.
    5. Matthews, Steven, 1987. "Comparing Auctions for Risk Averse Buyers: A Buyer's Point of View," Econometrica, Econometric Society, vol. 55(3), pages 633-646, May.
    6. Ning Sun & Zaifu Yang, 2006. "Equilibria and Indivisibilities: Gross Substitutes and Complements," Econometrica, Econometric Society, vol. 74(5), pages 1385-1402, September.
    7. Elena Grigorieva & P. Herings & Rudolf Müller & Dries Vermeulen, 2007. "The private value single item bisection auction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 30(1), pages 107-118, January.
    8. Mishra, Debasis & Parkes, David C., 2007. "Ascending price Vickrey auctions for general valuations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 335-366, January.
    9. Paul Klemperer, 2010. "The Product-Mix Auction: A New Auction Design for Differentiated Goods," Journal of the European Economic Association, MIT Press, vol. 8(2-3), pages 526-536, 04-05.
    10. Demange, Gabrielle & Gale, David & Sotomayor, Marilda, 1986. "Multi-Item Auctions," Journal of Political Economy, University of Chicago Press, vol. 94(4), pages 863-872, August.
    11. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    12. Mishra, Debasis & Talman, Dolf, 2010. "Characterization of the Walrasian equilibria of the assignment model," Journal of Mathematical Economics, Elsevier, vol. 46(1), pages 6-20, January.
    13. Lawrence M. Ausubel, 2004. "An Efficient Ascending-Bid Auction for Multiple Objects," American Economic Review, American Economic Association, vol. 94(5), pages 1452-1475, December.
    14. Andersson, Tommy & Erlanson, Albin, 2013. "Multi-item Vickrey–English–Dutch auctions," Games and Economic Behavior, Elsevier, vol. 81(C), pages 116-129.
    15. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    16. Sankaran, Jayaram K., 1994. "On a dynamic auction mechanism for a bilateral assignment problem," Mathematical Social Sciences, Elsevier, vol. 28(2), pages 143-150, October.
    17. Paul Milgrom, 2000. "Putting Auction Theory to Work: The Simultaneous Ascending Auction," Journal of Political Economy, University of Chicago Press, vol. 108(2), pages 245-272, April.
    18. de Vries, Sven & Schummer, James & Vohra, Rakesh V., 2007. "On ascending Vickrey auctions for heterogeneous objects," Journal of Economic Theory, Elsevier, vol. 132(1), pages 95-118, January.
    19. Gul, Faruk & Stacchetti, Ennio, 2000. "The English Auction with Differentiated Commodities," Journal of Economic Theory, Elsevier, vol. 92(1), pages 66-95, May.
    20. Gul, Faruk & Stacchetti, Ennio, 1999. "Walrasian Equilibrium with Gross Substitutes," Journal of Economic Theory, Elsevier, vol. 87(1), pages 95-124, July.
    21. Ning Sun & Zaifu Yang, 2009. "A Double-Track Adjustment Process for Discrete Markets With Substitutes and Complements," Econometrica, Econometric Society, vol. 77(3), pages 933-952, May.
    22. Maskin, Eric S & Riley, John G, 1984. "Optimal Auctions with Risk Averse Buyers," Econometrica, Econometric Society, vol. 52(6), pages 1473-1518, November.
    23. Albin Erlanson, 2014. "The Duo-Item Bisection Auction," Computational Economics, Springer;Society for Computational Economics, vol. 43(1), pages 15-31, January.
    24. Lawrence M. Ausubel, 2006. "An Efficient Dynamic Auction for Heterogeneous Commodities," American Economic Review, American Economic Association, vol. 96(3), pages 602-629, June.
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    More about this item

    Keywords

    Approximate auction; approximated preferences; non-quasi-linear preferences;
    All these keywords.

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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