Identification of time and risk preferences in buy price auctions

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 General Motors Assistance Corporation. 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 appeal 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. 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 conditions 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 cases where the variation in auction characteristics is more limited.

[1]  Gregory Lewis,et al.  Dynamic Demand Estimation in Auction Markets , 2016, Review of Economic Studies.

[2]  Neel Sundaresan,et al.  Assessing Sale Strategies in Online Markets Using Matched Listings , 2015 .

[3]  Rosa L. Matzkin.  Nonparametric Identification in Structural Economic Models , 2013 .

[4]  I. Perrigne,et al.  Identification of Insurance Models with Multidimensional Screening , 2015, 1508.02919.

[5]  José J. Canals-Cerdá,et al.  Arriving in Time: Estimation of English Auctions With a Stochastic Number of Bidders , 2012 .

[6]  Sandra Campo,et al.  Risk aversion and asymmetry in procurement auctions: Identification, estimation and application to construction procurements , 2012 .

[7]  Dorian Quint,et al.  Material SUPPLEMENT TO “ IDENTIFICATION AND INFERENCE IN ASCENDING AUCTIONS WITH CORRELATED PRIVATE VALUES , 2013 .

[8]  Neel Sundaresan,et al.  Learning from Seller Experiments in Online Markets , 2011 .

[9]  Q. Vuong,et al.  Semiparametric Estimation of First-Price Auctions with Risk Averse Bidders* , 2011 .

[10]  E. Krasnokutskaya,et al.  Identification and Estimation of Auction Models with Unobserved Heterogeneity , 2011 .

[11]  John Asker,et al.  A Study of the Internal Organization of a Bidding Cartel , 2010 .

[12]  Daniel W. Elfenbein,et al.  Charity as a Substitute for Reputation: Evidence from an Online Marketplace , 2010 .

[13]  Christopher Adams,et al.  The Sealed-Bid Abstraction in Online Auctions , 2009, Mark. Sci..

[14]  C. Adams.  Identifying Demand from Online Auction Data , 2009 .

[15]  James W. Roberts,et al.  Unobserved Heterogeneity and Reserve Prices in Auctions , 2009 .

[16]  Robin C. Sickles,et al.  An Analysis of Strategic Behavior in Ebay Auctions , 2009 .

[17]  Quang Vuong,et al.  Nonparametric Identification of Risk Aversion in First‐Price Auctions Under Exclusion Restrictions , 2009 .

[18]  F. Decarolis.  When the Highest Bidder Loses the Auction , 2009 .

[19]  Amit Gandhi,et al.  Identifying Preferences under Risk from Discrete Choices , 2009 .

[20]  Robert Zeithammer,et al.  Sequential Auctions with Information About Future Goods , 2008 .

[21]  K. Srinivasan,et al.  When auction meets fixed price: a theoretical and empirical examination of buy-it-now auctions , 2008 .

[22]  Jesús Fernández-Villaverde,et al.  Empirical Analysis of Dynamic Bidding on eBay ∗ , 2008 .

[23]  Christopher Adams.  Estimating demand from eBay prices , 2007 .

[24]  Robert Zeithammer,et al.  Research Note - Strategic Bid-Shading and Sequential Auctioning with Learning from Past Prices , 2007, Manag. Sci..

[25]  Jérémie Gallien,et al.  Temporary and Permanent Buyout Prices in Online Auctions , 2007, Manag. Sci..

[26]  Identification and Estimation of Bidders' Risk Aversion in First-Price Auctions , 2007 .

[27]  Philip A. Haile,et al.  Nonparametric Approaches to Auctions , 2007 .

[28]  John Asker.  A Study of the Internal Organisation of a Bidding Cartel ∗ , 2007 .

[29]  Denis Nekipelov.  Entry Deterrence and Learning Prevention on eBay ∗ , 2007 .

[30]  I. Perrigne,et al.  Estimating risk aversion from ascending and sealed-bid auctions: the case of timber auction data , 2008 .

[31]  Young-Hoon Park,et al.  Willingness to Pay and Competition in Online Auctions , 2007 .

[32]  Andrew B. Whinston,et al.  Buy-price English auction , 2006, J. Econ. Theory.

[33]  Brett Katzman,et al.  The role of varying risk attitudes in an auction with a buyout option , 2006 .

[34]  Robert Zeithammer.  Strategic Bid-Shading and Sequential Auctioning with Learning from Past Prices , 2006 .

[35]  Daniel A. Ackerberg,et al.  The Buy-it-now Option, Risk Aversion, and Impatience in an Empirical Model of eBay Bidding , 2006 .

[36]  Morten I. Lau,et al.  Eliciting Risk and Time Preferences , 2008 .

[37]  Robert Zeithammer.  Forward-Looking Bidding in Online Auctions , 2005 .

[38]  John Wooders,et al.  Auctions with a buy price , 2004 .

[39]  Identifying Demand in Ebay Auctions , 2004 .

[40]  Elena Krasnokutskaya,et al.  Identification and Estimation in Highway Procurement Auctions Under Unobserved Auction Heterogeneity , 2004 .

[41]  Igal Milchtaich,et al.  Random-player games , 2004, Games Econ. Behav..

[42]  Steven T. Anderson,et al.  Buy it Now: A Hybrid Internet Market Institution , 2004 .

[43]  Timothy Mathews,et al.  The Impact of Discounting on an Auction with a Buyout Option: a Theoretical Analysis Motivated by eBay’s Buy-It-Now Feature , 2004 .

[44]  Unjy Song,et al.  Nonparametric Estimation of an eBay Auction Model with an Unknown Number of Bidders* , 2004 .

[45]  Andreas Blume,et al.  All equilibria of the Vickrey auction , 2004, J. Econ. Theory.

[46]  Philip A. Haile,et al.  Inference with an Incomplete Model of English Auctions , 2000, Journal of Political Economy.

[47]  Hock-Hai Teo,et al.  Determinants of Buy-It-Now Auction Choice on eBay , 2003, PACIS.

[48]  Shuzhi Sam Ge,et al.  Adaptive NN control of uncertain nonlinear pure-feedback systems , 2002, Autom..

[49]  Q. Vuong,et al.  Structural Estimation of the Affliated Private Value Auction Model , 2002 .

[50]  Martin Pesendorfer,et al.  Estimation of a Dynamic Auction Game , 2001 .

[51]  Lisa N. Takeyama,et al.  Buy prices in online auctions: irrationality on the internet? , 2001 .

[52]  Ali Hortaçsu,et al.  Winner's Curse, Reserve Prices and Endogenous Entry: Empirical Insights from Ebay Auctions , 2003 .

[53]  Susan Athey,et al.  Identification of Standard Auction Models , 2000 .

[54]  Q. Vuong,et al.  Optimal Nonparametric Estimation of First-price Auctions , 2000 .

[55]  Bert Fristedt,et al.  A modern approach to probability theory , 1996 .

[56]  V. J. Hotz,et al.  Conditional Choice Probabilities and the Estimation of Dynamic Models , 1993 .

[57]  Michael Plum,et al.  Characterization and computation of nash-equilibria for auctions with incomplete information , 1992 .

[58]  O. Kallenberg.  Random Measures , 1983 .

[59]  Paul R. Milgrom,et al.  Rational Expectations, Information Acquisition, and Competitive Bidding , 1981 .