Large auctions with risk-averse bidders.

We study private-value auctions with n risk-averse bidders, where n is large. We first use asymptotic analysis techniques to calculate explicit approximations of the equilibrium bids and of the seller’s revenue in any k-price auction ( k = 1, 2, . . .). These explicit approximations show that in all large k-price auctions the effect of risk-aversion is O(1/ n2) small. Hence, all large k-price auctions with risk-averse bidders are O(1/ n2) revenue equivalent. The generalization, that all large auctions are O(1/ n2) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as $${n\longrightarrow \infty }$$ with risk-averse bidders is strictly below the risk-neutral limit. Therefore, these auction mechanisms are not revenue equivalent to large k-price auctions even to leading-order as $${n\longrightarrow \infty }$$. [ABSTRACT FROM AUTHOR]