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Unformatted text preview: Identification of Time and Risk Preferences in Buy Price Auctions Daniel Ackerberg * University of Michigan [email protected] Keisuke Hirano University of Arizona [email protected] Quazi Shahriar San Diego State University [email protected] April 27, 2011 Abstract Buy price auctions merge a posted price option with a standard bidding mechanisms, and have been used by various online auction sites including eBay and GMAC. A buyer in a buy price auction can accept the buy price to win with certainty and end the auction early. Intuitively, the buy price option may be appealing to bidders who are risk averse or impatient to obtain the good, and a number of authors have examined how such mechanisms can increase the seller’s expected revenue over standard auctions. We show that data from buy price auctions can be used to identify bidders’ risk aversion and time preferences. We develop a private value model of bidder behavior in a buy price auction with a temporary buy price. In our setup, bidders arrive stochastically over time, and the auction proceeds as a second-price sealed bid auction after the buy price disappears. Upon arrival, a bidder in our model is allowed to act immediately (i.e. accept the buy price if it is still available, or place a bid) or wait and act later. Allowing for general forms of risk aversion and impatience, we first characterize equilibria in cutoff strategies and describe the condition under which all symmetric pure-strategy subgame- perfect Bayesian Nash equilibria are in cutoff strategies. Given sufficient exogenous variation in auction characteristics such as reserve and buy prices and in auction lengths, we then show that the arrival rate, valuation distribution, utility function, and time-discounting function in our model are all nonparametrically identified. We also develop extensions of the identification results for settings in which the variation in auction characteristics is more limited. * We thank Martin Dufwenberg, Jin Hahn, Phil Haile, Greg Lewis, Isabelle Perrigne, Bernard Salani´ e, Quang Vuong, John Wooders, Robert Zeithammer, and seminar participants at U. of Arizona, UC Irvine, UCLA, Carnegie Mellon U., Columbia U., Brown U., Harvard U., U. of Michigan, U. of South Florida, Yale U., and the Conference on Identification of Demand at Brown University for comments and suggestions. Special thanks are due to Robert Ackerberg for particularly helpful discussions. All errors are our own. 1 1 Introduction This paper studies identification of bidder preferences in single unit buy price (BP) auctions. BP auctions merge a posted price selling environment with an auction environment, and have been used by eBay (in their “Buy-it-Now” auctions), GMAC, and other organizations as an alternative to standard first or second price auctions. We show that data from BP auctions can be particularly informative about risk aversion and time preferences among potential bidders, in a way that stan- dard auctions are not. As a result, it is possible to recover bidder preferences from widely availabledard auctions are not....
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This note was uploaded on 12/26/2011 for the course ECON 245a taught by Professor Staff during the Fall '08 term at UCSB.
- Fall '08