Equilibrium Existence in First‐Price Auctions With Private Values
Abstract
We provide sufficient conditions for equilibrium existence in first‐price auctions with private values that accommodate non quasi‐linear utilities and value‐distributions that contain atoms and exhibit positive or negative correlation. These conditions show that equilibrium existence often turns on properties of a single statistic of the joint distribution of values, namely, the minimum value in the support of the high‐value distribution (the mHV). We also show that modifying the standard tie‐breaking rule only at the mHV is enough to guarantee equilibrium existence without our sufficient conditions. Our results also apply to Bertrand price competition when each firm's constant marginal cost is private information.
Fields of Study & Subjects
Auction Theory and Applications
Consumer Market Behavior and Pricing
Game Theory and Applications
Publication details
- Journal / source
- Econometrica
- Publisher
- The Econometric Society
- Volume
- 94
- Issue
- 1
- Pages
- 193–224
- Publication date
- 1 January 2026
- Language
- EN