Optimal takeover contests with toeholds

This paper characterizes how a target firm should be sold when the possible buyers (bidders) have prior stakes in its ownership (toeholds). We find that the optimal mechanism needs to be implemented by a non-standard auction which imposes a bias against bidders with high toeholds. This discriminatory procedure is such that the target´s average sale price is increasing in both the size of the common toehold and the degree of asymmetry in these stakes. It is also shown that a simple mechanism of sequential negotiation replicates the main properties of the optimal procedure and yields a higher average selling price than the standard auctions commonly used in takeover battles

Optimal Crowdsourcing Contests

We study the design and approximation of optimal crowdsourcing contests. Crowdsourcing contests can be modeled as all-pay auctions because entrants must exert effort up-front to enter. Unlike all-pay auctions where a usual design objective would be to maximize revenue, in crowdsourcing contests, the principal only benefits from the submission with the highest quality. We give a theory for optimal crowdsourcing contests that mirrors the theory of optimal auction design: the optimal crowdsourcing contest is a virtual valuation optimizer (the virtual valuation function depends on the distribution of contestant skills and the number of contestants). We also compare crowdsourcing contests with more conventional means of procurement. In this comparison, crowdsourcing contests are relatively disadvantaged because the effort of losing contestants is wasted. Nonetheless, we show that crowdsourcing contests are 2-approximations to conventional methods for a large family of "regular" distributions, and 4-approximations, otherwise.Comment: The paper has 17 pages and 1 figure. It is to appear in the proceedings of ACM-SIAM Symposium on Discrete Algorithms 201

The Amsterdam Auction

Auctions used to sell houses often attract a diverse group of bidders, with realtors and speculators out for a bargain competing against buyers with a real interest in the house. Value asymmetries such as these necessitate careful consideration of the auction format as revenue equivalence cannot be expected to hold. From a theoretical viewpoint, Myerson's (1981) mechanism design approach has identified the seller's optimal choice. The proposed mechanism entails assigning credits to weaker bidders to promote competition and setting bidder-specific reserve prices. In practice, however, sellers often lack the detailed information needed to choose credits and reserve prices optimally, nor can they always discriminate among bidders. A more practical solution to the seller's problem is suggested by the "Amsterdam auction," where a premium is offered to encourage weak bidders to compete aggressively. This auction format, which has been used to sell houses in Amsterdam for centuries, treats all bidders the same and does not rely on detailed information about their value-distributions. In this paper, we consider premium auctions like the one in Amsterdam and demonstrate their revenue-generating virtues in asymmetric situations. We report the results of an experiment, which compares the standard first-price and English formats with two premium auctions in symmetric and asymmetric settings. The introduction of a premium leads weak bidders to set an endogenous reserve price for stronger rivals, with a dramatic effect on the sales price. Awarding a premium raises revenues, especially since Bertrand competition between weaker bidders virtually dissipates the premium to be paid.Auctions, experiments, asymmetries, premium

On the Concentration of Allocations and Comparisons of Auctions in Large Economies

We analyze competitive pressures in a sequence of auctions with a growing number of bidders, in a model that includes private and common valuations as special cases. We show that the key determinant of bidders' surplus (and implicitly auction revenue) is how the goods are distributed. In any setting and sequence of auctions where the allocation of good(s) is concentrated among a shrinking proportion of the population, the winning bidders enjoy no surplus in the limit. If instead the good(s) are allocated in a dispersed manner so that a non- vanishing proportion of the bidders obtain objects, then in any of a wide class of auctions bidders enjoy a surplus that is bounded away from zero. Moreover, under dispersed allocations, the format of the auction matters. If bidders have constant marginal utilities for objects up to some limit, then uniform price auctions lead to higher revenue than discriminatory auctions. If agents have decreasing marginal utilities for objects, then uniform price auctions are asymptotically efficient, while discriminatory auctions are asymptotically {\sl in}efficient. Finally, we show that in some cases where dispersed allocations are efficient, revenue may increase by bundling goods at the expense of efficiency.Auction, Competition, Mechanism, Asymptotic Efficiency, Revenue Equivalence

Auctions: Theory and Practice

Governments use them to sell everything from oilfields to pollution permits, and to privatize companies; consumers rely on them to buy baseball tickets and hotel rooms, and economic theorists employ them to explain booms and busts. Auctions make up many of the world's most important markets; and this book describes how auction theory has also become an invaluable tool for understanding economics. Auctions: Theory and Practice provides a non-technical introduction to auction theory, and emphasises its practical application. Although there are many extremely successful auction markets, there have also been some notable fiascos, and Klemperer provides many examples. He discusses the successes and failures of the one-hundred-billion dollar "third-generation" mobile-phone license auctions; he, jointly with Ken Binmore, designed the first of these. Klemperer also demonstrates the surprising power of auction theory to explain seemingly unconnected issues such as the intensity of different forms of industrial competition, the costs of litigation, and even stock trading 'frenzies' and financial crashes. Engagingly written, the book makes the subject exciting not only to economics students but to anyone interested in auctions and their role in economics.markets, industrial competition, litigation, stock trading, financial crashes

Economic Insights from Internet Auctions: A Survey

This paper surveys recent studies of Internet auctions. Four main areas of research are summarized. First, economists have documented strategic bidding in these markets and attempted to understand why sniping, or bidding at the last second, occurs. Second, some researchers have measured distortions from asymmetric information due, for instance, to the winner's curse. Third, we explore research about the role of reputation in online auctions. Finally, we discuss what Internet auctions have to teach us about auction design.

Mixed Bundling Auctions

We study multi-object auctions where agents have private and additive valuations for heterogeneous objects. We focus on the revenue properties of a class of dominant strategy mechanisms where a weight is assigned to each partition of objects. The weights influence the probability with which partitions are chosen in the mechanism. This class contains efficient auctions, pure bundling auctions, mixed bundling auctions, auctions with reserve prices and auctions with pre-packaged bundles. For any number of objects and bidders, both the pure bundling auction and separate, efficient auctions for the single objects are revenue-inferior to an auction that involves mixed bundling

Know thy enemies : knowledge of rivals' types and its effect on auctions

auctions

Optimal takeover contests with toeholds

This paper characterizes how a target firm should be sold when the possible buyers (bidders) have prior stakes in its ownership (toeholds). We find that the optimal mechanism needs to be implemented by a non-standard auction which imposes a bias against bidders with high toeholds. This discriminatory procedure is such that the target´s average sale price is increasing in both the size of the common toehold and the degree of asymmetry in these stakes. It is also shown that a simple mechanism of sequential negotiation replicates the main properties of the optimal procedure and yields a higher average selling price than the standard auctions commonly used in takeover battles.Optimal auctions, Takeovers, Toeholds, Asymmetric auctions

A Note on Revenue Effects of Asymmetry in Private-Value Auctions

We formulate a way to study whether the asymmetry of buyers (in the sense of having different prior probability distributions of valuations) is helpful to the seller in private-value auctions (asked first by Cantillon [2001]). In our proposed formulation, this question corresponds to two important questions previously asked: Does a first-price auction have higher revenue than a second-price auction when buyers have asymmetric distributions (asked by Maskin and Riley[2000])? And does a seller enhance revenue by releasing information (asked by Milgrom and Weber[1982])? This is shown by constructing two Harsanyi games of incomplete information each having the same ex-ante distribution of valuations but in one beliefs are symmetric while in the other beliefs are sometimes asymmetric. Our main result is that answers to all three questions coincide when values are independent and are related when values are affiliated.Asymmetric Auctions; Asymmetric Beliefs; Affiliation; Linkage Principle