Abstract
We consider discriminatory auctions for multiple identical units of a good. Players have private values, possibly for multiple units. None of the usual assumptions about symmetry of players' distributions over values or symmetry of equilibrium play are made. Because of this, equilibria will typically involve inefficient allocations. Equilibria also become very difficult to solve for. Using an approach which does not depend on explicit equilibrium calculations we show that such auctions become arbitrarily close to efficient as the number of players, and possibly the number of objects, grows large, and provide a simple characterization of limit equilibria.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 509-528 |
| Number of pages | 20 |
| Journal | Review of Economic Studies |
| Volume | 66 |
| Issue number | 3 |
| DOIs | |
| State | Published - Jul 1999 |
Funding
Consider choosing both iE {I, ... , n} and hE {I, ... m}, at random. Then, by (A4), there is n* < 00 such that for n > n*, vi(h) is above v* = (r + v)/2 with probability at least M(v- v*)/m, and so E(vih) is at least M(v- v*)v*/ m=:t;. If objects are randomly allocated across both players and units of demand, then expected surplus is at least knt;. Since under efficient allocation, the k" objects go to the k" highest values, E(r) is at least this amount, and we are done. II Acknowledgements. I thank Eddie Dekel, Elchanan Ben-Porath, Joseph Harrington, Peter KlibanofT, Roger Myerson, Hyun Song Shin, Bob Weber, and three referees for helpful comments. Tianxiang Ye provided helpful comments and assistance in preparing the manuscript. I also thank seminar audiences at the University of Iowa, Johns Hopkins University, the University of Wisconsin, Northwestern University, the University of British Columbia and the Stony Brook Summer Game Theory workshop. Financial support from the NSF is gratefully acknowledged.
ASJC Scopus subject areas
- Economics and Econometrics