TY - JOUR

T1 - Competing auctions with endogenous quantities

AU - Moldovanu, Benny

AU - Sela, Aner

AU - Shi, Xianwen

N1 - Funding Information:
We wish to thank Stefan Behringer, Drew Fudenberg, Phil Haile, two anonymous referees and an associate editor for very helpful comments. We are grateful for the financial support from the German Science Foundation (SFB TR-15), the Max Planck Society, and the Humboldt Foundation.

PY - 2008/7/1

Y1 - 2008/7/1

N2 - Two sellers decide on their discrete supply of a homogenous good. There is a finite number of buyers with unit demand and privately known valuations. In the first model, there is a centralized market place where a uniform auction takes place. In the second, there are two distinct auction sites, each with one seller, and buyers decide where to bid. Using the theory of potential games, we show that in the one-site auction model there is always an equilibrium in pure-strategies. In contrast, if the distribution of buyers values has an increasing failure rate, and if the marginal cost of production is relatively low, there is no pure-strategy equilibrium where both sellers make positive profits in the competing sites model. We also identify conditions under which an equilibrium with a unique active site exists. We deal with the finite and discrete models by using several results about order statistics developed by Richard Barlow and Frank Proschan [R. Barlow, F. Proschan, Mathematical Theory of Reliability, Wiley, New York, 1965; R. Barlow, F. Proschan, Inequalities for linear combinations of order statistics from restricted families, Ann. Math. Statist. 37 (1966) 1593-1601; R. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, McArdle Press, Silver Spring, 1975].

AB - Two sellers decide on their discrete supply of a homogenous good. There is a finite number of buyers with unit demand and privately known valuations. In the first model, there is a centralized market place where a uniform auction takes place. In the second, there are two distinct auction sites, each with one seller, and buyers decide where to bid. Using the theory of potential games, we show that in the one-site auction model there is always an equilibrium in pure-strategies. In contrast, if the distribution of buyers values has an increasing failure rate, and if the marginal cost of production is relatively low, there is no pure-strategy equilibrium where both sellers make positive profits in the competing sites model. We also identify conditions under which an equilibrium with a unique active site exists. We deal with the finite and discrete models by using several results about order statistics developed by Richard Barlow and Frank Proschan [R. Barlow, F. Proschan, Mathematical Theory of Reliability, Wiley, New York, 1965; R. Barlow, F. Proschan, Inequalities for linear combinations of order statistics from restricted families, Ann. Math. Statist. 37 (1966) 1593-1601; R. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, McArdle Press, Silver Spring, 1975].

KW - Competing auctions

KW - Order statistics

UR - http://www.scopus.com/inward/record.url?scp=44949092213&partnerID=8YFLogxK

U2 - 10.1016/j.jet.2007.09.001

DO - 10.1016/j.jet.2007.09.001

M3 - Article

AN - SCOPUS:44949092213

SN - 0022-0531

VL - 141

SP - 1

EP - 27

JO - Journal of Economic Theory

JF - Journal of Economic Theory

IS - 1

ER -