Comparing Auctions for Risk Averse Buyers: A Buyer's Point of View

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. The interim preferences of buyers over three forms of auction are determined. The buyers are risk averse and ex ante identical, have private values, and are unaware at the time they bid of how many others are eligible to bid. The auctions compared are a second-price auction (SPA), a first-price auction (FPA), and a first-price auction conducted under a policy of revealing to the eligible bidders their actual number (FPA-R). If their types are independently distributed, the buyers prefer the SPA to the FPA-R to the FPA if they exhibit decreasing absolute risk aversion, and they are indifferent between all three auctions if they have constant absolute risk aversion. Their preferences are biased away from the SPA if their types are affiliated: they then prefer the FPA to the SPA if they exhibit constant absolute risk aversion, and the comparison is ambiguous if they exhibit decreasing absolute risk aversion. Affiliation also biases the buyer's preferences toward, and the seller's preferences away from, the revealing policy: assuming constant or decreasing or no risk aversion, the buyers prefer the FPA-R to the FPA, and the expected price is greater in the FPA than the FPA-R.

Information Aggregation in Auctions with an Unknown Number of Bidders

“…However, if the seller could vary the quantity sold, 4 he could adjust it in accordance with the number of bids submitted (once bids are submitted, the seller does not face uncertainty as to the number of submissions); for example, the seller could precommit to sell k i objects if n i bids are submitted. Regardless of its practical implications and feasibility, this more general setting highlights a crucial condition for information aggregation: at the moment of bid submission, bidders do not have to know the number of bidders or the number of objects; however, for information to 3 This exogenous randomness is specified as in Matthews' (1987) model of private-values auctions and Harstad et al's (1990) model of common-value auctions. Both of those papers considered only a singleobject setting with independently drawn private information.…”

“…. = k M = 1 has been studied in Matthews (1987) and Harstad et al (1990). 8 We treat the seller as able to demonstrate ex post to suspicious bidders the number of bids submitted,…”

“…Using Matthews (1987), the probability of n i bidders is π i n i /n, wheren = M i=1 π i n i . Denote by g(v|x) the distribution of v given x, which by Bayes' Theorem is:…”

Information aggregation in auctions with an unknown number of bidders

“…22 Note that, in the independent private-values setting, the assumption that the number of bidders is known is rather innocuous: bidding strategies directly extend to the case of an unknown number of bidders, and revenue equivalence holds (Matthews, 1987). In the common-value setting, on the contrary, this assumption significantly changes the picture of symmetric equilibrium bidding strategies and information aggregation properties.…”

Identification and Estimation in First-Price Auctions with Risk-Averse Bidders and Selective Entry

“…As is well known, risk aversion influences answers to a wide range of fundamental questions in auction design, such as choice of auction format (Maskin and Riley (1984)), structure of the optimal mechanism (Matthews (1987)), and whether to disclose reserve prices (Li and Tan (2000)). This in turn has motivated a substantial body of empirical work on risk aversion in real-world auctions, with available evidence strongly confirming its relevance in practice.…”