Large auctions with risk-averse bidders |
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Authors: | Gadi Fibich Arieh Gavious |
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Affiliation: | (1) NUS Business School, BIZ 1 Building #04-19, 1 Business Link, Singapore, 117592, Singapore;(2) Department of MIS, Central Connecticut State University, 1615 Stanley Street, New Britain, CT 06050, USA |
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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 ${nlongrightarrow infty }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? ¥{nlongrightarrow 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? ¥{nlongrightarrow infty }. |
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