Optimal Design Of English Auctions With Discrete Bid Levels

This paper considers a form of ascending price English auction widely used in both live and online auctions. This discrete bid auction requires that the bidders submit bids at predetermined discrete bid levels, and thus, there exists a minimal increment by which the bid price may be raised. In contrast, the academic literature of optimal auction design deals almost solely with continuous bid auctions. As a result, there is little practical guidance as to how an auctioneer, seeking to maximize its revenue, should determine the number and value of these discrete bid levels, and it is this omission that is addressed here. To this end, a model of a discrete bid auction from the literature is considered, and an expression for the expected revenue of this auction is derived. This expression is used to determine both numerical and analytical solutions for the optimal bid levels, and uniform and exponential bidder’s valuation distributions are compared. Finally, the limiting case where the number of discrete bid levels is large is considered. An analytical expression for the distribution of the optimal discrete bid levels is derived, and an intuitive understanding of how this distribution maximizes the revenue of the auction is developed

On the Inefficiency of the Uniform Price Auction

We present our results on Uniform Price Auctions, one of the standard sealed-bid multi-unit auction formats, for selling multiple identical units of a single good to multi-demand bidders. Contrary to the truthful and economically efficient multi-unit Vickrey auction, the Uniform Price Auction encourages strategic bidding and is socially inefficient in general. The uniform pricing rule is, however, widely popular by its appeal to the natural anticipation, that identical items should be identically priced. In this work we study equilibria of the Uniform Price Auction for bidders with (symmetric) submodular valuation functions, over the number of units that they win. We investigate pure Nash equilibria of the auction in undominated strategies; we produce a characterization of these equilibria that allows us to prove that a fraction 1-1/e of the optimum social welfare is always recovered in undominated pure Nash equilibrium -- and this bound is essentially tight. Subsequently, we study the auction under the incomplete information setting and prove a bound of 4-2/k on the economic inefficiency of (mixed) Bayes Nash equilibria that are supported by undominated strategies.Comment: Additions and Improvements upon SAGT 2012 results (and minor corrections on the previous version

Designing and Executing a Fair Revlon Auction

The author analyzes the role of corporate boards of directors during takeover and control transactions, specifically in regards to auctions. Courts have consistently considered unfair auction attempts in light of the importance of the business judgment rule. The author examines Delaware case law and highlights the Revlon case, which holds that once an auction begins, the board’s duty shifts from preservation of the corporate entity to maximization of value shareholders will receive from the sale. The author argues that a good understanding of auction theory will not only give courts a better perspective through which to examine directors’ actions but also will give directors more information on how to run auctions and respond to bids

Designing and Executing a Fair Revlon Auction

The author analyzes the role of corporate boards of directors during takeover and control transactions, specifically in regards to auctions. Courts have consistently considered unfair auction attempts in light of the importance of the business judgment rule. The author examines Delaware case law and highlights the Revlon case, which holds that once an auction begins, the board’s duty shifts from preservation of the corporate entity to maximization of value shareholders will receive from the sale. The author argues that a good understanding of auction theory will not only give courts a better perspective through which to examine directors’ actions but also will give directors more information on how to run auctions and respond to bids