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.