The existing literature on optimal auctions focuses on optimizing the expected revenue of the seller, and is appropriate for risk-neutral sellers. In this paper, we identify good mechanisms for risk-averse sellers. As is standard in the economics literature, we model the risk-aversion of a seller by endowing the seller with a monotone concave utility function. We then seek robust mechanisms that are approximately optimal for all sellers, no matter what their levels of risk-aversion are. We have two main results for multi-unit auctions with unit-demand bidders whose valuations are drawn i.i.d. from a regular distribution. First, we identify a posted-price mechanism called the Hedge mechanism, which gives a universal constant factor approximation; we also show for the unlimited supply case that this mechanism is in a sense the best possible. Second, we show that the VCG mechanism gives a universal constant factor approximation when the number of bidders is even only a small multiple of the number of items. Along the way we point out that Myerson's characterization of the optimal mechanisms fails to extend to utility-maximization for risk-averse sellers, and establish interesting properties of regular distributions and monotone hazard rate distributions.
There is some work that deals with risk in the context of auctions. Eso @cite_15 identifies an optimal mechanism for a risk-averse seller, which always provides the same revenue bid vector by modifying Myerson's optimal mechanism; unfortunately, this mechanism does not satisfy ex-post (or even ex-interim) individual rationality, and charges bidders even when they lose. Maskin and Riley @cite_7 identifies the optimal Bayesian-incentive compatible mechanism for a risk-neutral seller when the are risk-averse. In our model, we identify mechanisms that are ex-post incentive compatible. So the buyers optimize their utility bidding truthfully for every realization of the valuations, and thus have no uncertainty or risk to deal with. @cite_0 studies risk-aversion in single-item auctions. Specifically, they show for both the first and second price mechanisms that the optimal reserve price reduces as the level of risk-aversion of the seller increases. In contrast, we identify the optimal truthful mechanism for a risk-averse seller in a single-item auction in (it happens to be a second price mechanism with a reserve), study auctions of two or more items and identify mechanisms that are simultaneously approximate for all risk-averse sellers.
@cite_0 @cite_15 @cite_7
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This paper analyzes the effects of buyer and seller risk aversion in first and second-price auctions. The setting is the classic one of symmetric and independent private values, with ex ante homogeneous bidders. However, the seller is able to optimally set the reserve price. In both auctions the seller’s optimal reserve price is shown to decrease in his own risk aversion, and more so in the first-price auction. Thus, greater seller risk aversion increases the ex post efficiency of both auctions, and especially that of the first-price auction. The seller’s optimal reserve price in the first-price, but not in the second-price, auction decreases in the buyers’ risk aversion. Thus, greater buyer risk aversion also increases the ex post efficiency of the first but not the second-price auction. At the interim stage, the first-price auction is preferred by all buyer types in a lower interval, as well as by the seller. Abstract We consider auctions with a risk averse seller in independent private values environments with risk neutral buyers. We show that for every incentive compatible selling mechanism there exists a mechanism which provides deterministically the same (expected) revenue.