### abstract

- 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/n 2) small. Hence, all large k-price auctions with risk-averse bidders are O(1/n 2) revenue equivalent. The generalization, that all large auctions are O(1/n 2) revenue equivalent, is false. Indeed, we show that there exist auction mechanisms for which the limiting revenue as n® ¥{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® ¥{n\longrightarrow \infty }. KeywordsLarge auctions-Risk aversion-Asymptotic analysis-Revenue equivalence-Equilibrium strategy