Auction Theory, 2nd Edition

304 Existence of Equilibrium in First-Price Auctions

example, with risk aversion or affiliated private values. For asymmetric inter-

dependent values with affiliated signals, however, this technique is applicable

to only the case of two bidders. Reny and Zamir (2004) have, however, suc-

ceeded in developing an existence result in this environment that applies with

an arbitrary number of bidders.

Other papers that establish the existence of an equilibrium in first-price

auctions using discrete approximation techniques—either by discretizing the

set of values or, as above, the set of possible bids—include Lebrun (1996) and

Maskin and Riley (2000b). Reny