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 → ∞ 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 → ∞.