English Auctions and Walrasian Equilibria with Multiple Objects: a dynamic approach
This paper studies the English (progressive) auction for an exchange economy with multiple objects. The English auction is a tatonnement process and lasts multiple rounds. It is modeled as a sequence of round games. Each round game is a normal form game in which an agent's strategies are his bids and his payoff is his trading profits of his winning bundle at that round. Among all these normal form games, all intermediary round games are in fact the ''virtual'' games because the payoffs to agents are not finalized unless the auction closes. We show that any ascending price sequence obtained from the English auction converges to a Walrasian equilibrium (if any) within finite rounds when agents submit their bids that consist of a Nash equilibrium in each round game. We also provide a sufficient condition for the English auction to converge to a Walrasian equilibrium in finite rounds. But this condition is weaker than the Nash equilibrium. This shows that the Nash equilibrium is not necessary (though sufficient) for the English auction to converge to a Walrasian equilibrium.
|Date of creation:||01 Apr 1997|
|Contact details of provider:|| Postal: New Jersey Hall - 75 Hamilton Street, New Brunswick, NJ 08901-1248|
Phone: (732) 932-7363
Fax: (732) 932-7416
Web page: http://economics.rutgers.edu/
More information through EDIRC
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Rubinstein, Ariel, 1982.
"Perfect Equilibrium in a Bargaining Model,"
Econometric Society, vol. 50(1), pages 97-109, January.
- Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 661465000000000387, David K. Levine.
- Ariel Rubinstein, 2010. "Perfect Equilibrium in a Bargaining Model," Levine's Working Paper Archive 252, David K. Levine.
- Paul R. Milgrom, 1985. "Auction Theory," Cowles Foundation Discussion Papers 779, Cowles Foundation for Research in Economics, Yale University.
- Bulow, Jeremy & Klemperer, Paul, 1996. "Auctions versus Negotiations," American Economic Review, American Economic Association, vol. 86(1), pages 180-194, March.
- Crawford, Vincent P & Knoer, Elsie Marie, 1981. "Job Matching with Heterogeneous Firms and Workers," Econometrica, Econometric Society, vol. 49(2), pages 437-450, March.
- Wilson, Robert, 1992. "Strategic analysis of auctions," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 8, pages 227-279 Elsevier.
- Ma, Jinpeng, 1998. "Competitive Equilibrium with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 82(2), pages 458-468, October.
- Jinpeng Ma, 1998. "Competitive Equilibrium with Indivisibilities," Departmental Working Papers 199809, Rutgers University, Department of Economics.
- Peter Cramton, 2002. "Spectrum Auctions," Papers of Peter Cramton 01hte, University of Maryland, Department of Economics - Peter Cramton, revised 16 Jul 2001.
- 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.
- Gabrielle Demange & Gale David & Marilda Sotomayor, 1986. "Multi-Item Auctions," Post-Print halshs-00670982, HAL.
- Milgrom, Paul R & Weber, Robert J, 1982. "A Theory of Auctions and Competitive Bidding," Econometrica, Econometric Society, vol. 50(5), pages 1089-1122, September.
- Paul Milgrom & Robert J. Weber, 1981. "A Theory of Auctions and Competitive Bidding," Discussion Papers 447R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
- Gul, F. & Stacchetti, E., 1997. "Walrasian Equilibrium Without Complementarities," Papers 97-03, Michigan - Center for Research on Economic & Social Theory.
- Bikhchandani, Sushil & Mamer, John W., 1997. "Competitive Equilibrium in an Exchange Economy with Indivisibilities," Journal of Economic Theory, Elsevier, vol. 74(2), pages 385-413, June.
- John McMillan, 1994. "Selling Spectrum Rights," Journal of Economic Perspectives, American Economic Association, vol. 8(3), pages 145-162, Summer.
- 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.
- McAfee, R Preston & McMillan, John, 1987. "Auctions and Bidding," Journal of Economic Literature, American Economic Association, vol. 25(2), pages 699-738, June. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:rut:rutres:199702. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.