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

Steven Matthews

Abstract

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.