Theories on Auctions with Participation Costs

In this dissertation I study theories on auctions with participation costs with various information structure. Chapter II studies equilibria of second price auctions with differentiated participation costs. We consider equilibria in independent private values environments where bidders? entry costs are common knowledge while valuations are private information. We identify two types of equilibria: monotonic equilibria in which a higher participation cost results in a higher cutoff point for submitting a bid, and neg-monotonic equilibria in which a higher participation cost results in a lower cutoff point. We show that there always exists a monotonic equilibrium, and further, that the equilibrium is unique for concave distribution functions and strictly convex distribution functions with some additional conditions. There exists a neg-monotonic equilibrium when the distribution function is strictly convex and the difference of the participation costs is sufficiently small. We also provide comparative static analysis and study the limit status of equilibria when the difference in bidders' participation costs approaches zero. Chapter III studies equilibria of second price auctions when values and participation costs are both privation information and are drawn from general distribution functions. We consider the existence and uniqueness of equilibrium. It is shown that there always exists an equilibrium for this general economy, and further there exists a unique symmetric equilibrium when all bidders are ex ante homogenous. Moreover, we identify a sufficient condition under which we have a unique equilibrium in a heterogeneous economy with two bidders. Our general framework covers many relevant models in the literature as special cases. Chapter IV characterizes equilibria of first price auctions with participation costs in the independent private values environment. We focus on the cutoff strategies in which each bidder participates and submits a bid if his value is greater than or equal to a critical value. It is shown that, when bidders are homogenous, there always exists a unique symmetric equilibrium, and further, there is no other equilibrium when valuation distribution functions are concave. However, when distribution functions are elastic at the symmetric equilibrium, there exists an asymmetric equilibrium. We find similar results when bidders are heterogenous

Equilibria in Asymmetric Auctions with Entry

Regarding optimal design in the private value environment, there is an unsolved discrepancy in the literature regarding asymmetric auctions and auctions with endogenous participation; Literature on the former suggests that well-designed distortive mechanisms are optimal (revenue maximizing) assuming the bidding costs are negligible, while that on the latter insists that the mechanisms with free entry and no distortion are optimal provided that the potential bidders are ex ante symmetric.This paper is the first attempt to reconcile the two views by establishing a model for asymmetric auctions with costly participation. The main findings are threefold; First, an optimal outcome is possible if and only if the mechanism is ex post efficient. Second, without any participation control, a coordination problem is likely in which only the weak bidders participate and the strong bidders stay out. Finally, there is an entry fee/subsidization scheme which, together with an ex post efficient mechanism, induces the optimal outcome as a unique equilibrium.

Set-Asides and Subsidies in Auctions

Set-asides and subsidies are used extensively in government procurement and natural resource sales. We analyze these policies in an empirical model of U.S. Forest Service timber auctions. The model fits the data well both within the sample of unrestricted sales where we estimate the model, and when we predict (out of sample) bidder entry and prices for small business set-asides. Our estimates suggest that restricting entry to small businesses substantially reduces efficiency and revenue, although it does increase small business participation. An alternative policy of subsidizing small bidders would increase revenue and small bidder profit, while eliminating almost all of the efficiency loss of set-asides, and only slightly decreasing the profit of larger firms. We explain these findings by connecting to the theory of optimal auction design.set-asides, subsidies, natural resources, timber, auctions

"Upping the ante": How to design efficient auctions with entry?

In the symmetric independent private value model, we revisit auctions with entry by adding two additional ingredients: difficulties to commit to the announced mechanism, in particular not to update the reserve price after bidders took their entry decisions, and seller's ex ante uncertainty on her reservation value which calls for flexibility. Shill bidding or ex post rights to cancel the sale may provide some valuable flexibility in second price auctions. However, both fail to be efficient since the seller may keep the good while it would be efficient to allocate it to the highest bidder. The English auction with jump bids and cancelation rights is shown to implement the first best in large environments. On the positive side, special emphasis is put on the equilibrium analysis of auctions with shill bidding and on a variety of associated new insights including counterintuitive comparative statics and a comparison with posted-prices.auctions ; auctions with entry ; shill bidding ; commitment failure ; hold-up ; posted-price ; cancelation rights ; jump bids ; bilateral asymmetric information

Allocative and Informational Externalities in Auctions and Related Mechanisms

We study the effects of allocative and informational externalities in (multi-object) auctions and related mechanisms. Such externalities naturally arise in models that embed auctions in larger economic contexts. In particular, they appear when there is downstream interaction among bidders after the auction has closed. The endogeneity of valuations is the main driving force behind many new, specific phenomena with allocative externalities: even in complete information settings, traditional auction formats need not be efficient, and they may give rise to multiple equilibria and strategic non-participation. But, in the absence of informational externalities, welfare maximization can be achieved by Vickrey-Clarke- Groves mechanisms. Welfare-maximizing Bayes-Nash implementation is, however, impossible in multi-object settings with informational externalities, unless the allocation problem is separable across objects (e.g. there are no allocative externalities nor complementarities) or signals are one-dimensional. Moreover, implementation of any choice function via ex-post equilibrium is generically impossible with informational externalities and multidimensional types. A theory of information constraints with multidimensional signals is rather complex, but indispensable for our study

Optimal Auctions with Simultaneous and Costly Participation

We study the optimal auction problem with participation costs in the symmetric independent private values setting, where bidders know their valuations when they make independent participation decisions. After characterizing the optimal auction in terms of participation cutoffs, we provide an example where it is asymmetric. We then investigate when the optimal auction will be symmetric/asymmetric and the nature of possible asymmetries. We also show that, under some conditions, the seller obtains her maximal profit in an (asymmetric) equilibrium of an anonymous second price auction. In general, the seller can also use non-anonymous auctions that resemble the ones that are actually observed in practice.

Endogenous Competition Alters the Structure of Optimal Auctions

Potential bidders respond to a sellerfs choice of auction mechanism for a common-value or affiliated-values asset by endogenous decisions whether to incur an information-acquisition cost (and observe a private estimate), or forgo competing. Privately informed participants decide whether to incur a bid-preparation cost and pay an entry fee, or cease competing. Auction rules and information flows are quite general; participation decisions may be simultaneous or sequential. The resulting revenue identity for any auction mechanism implies that optimal auctions are allocatively efficient; a nontrivial reserve price is revenue-inferior. Optimal auctions are otherwise contentless: any auction that sells without reserve becomes optimal by adjusting any one of the continuous, spanning parameters, e.g., the entry fee. Sellerfs surplus-extracting tools are now substitutes, not complements. Many econometric studies of auction markets are seen to be flawed in their identification of the number of bidders.

Empirical Models of Auctions

Many important economic questions arising in auctions can be answered only with knowledge of the underlying primitive distributions governing bidder demand and information. An active literature has developed aiming to estimate these primitives by exploiting restrictions from economic theory as part of the econometric model used to interpret auction data. We review some highlights of this recent literature, focusing on identification and empirical applications. We describe three insights that underlie much of the recent methodological progress in this area and discuss some of the ways these insights have been extended to richer models allowing more convincing empirical applications. We discuss several recent empirical studies using these methods to address a range of important economic questions.Auctions, Identification, Estimation, Testing

Endogenous entry and auctions design with private participation costs

This paper studies endogenous entry and ex ante revenue-maximizing auctions in an independent private value setting where potential bidders have private-information entry costs. The contribution of this paper is four-fold. First, we show that any equilibrium entry can be characterized through a set of continuous and monotonic shutdown curves that separate the bidders' types into participating and nonparticipating categories. Second, the expected winning probability of a participant does not depend on his private entry cost. Furthermore, the expected winning probabilities of the participating types are given by the slopes of the shutdown curves. Third, symmetric entry equilibria (shutdown curves) implemented by the classes of ex post efficient or ex post revenue-maximizing mechanisms are completely characterized. Fourth, within these two classes of mechanisms, a modified Vickrey auction with uniform reserve price and entry subsidy is ex ante revenue-maximizing. The desired entry subsidy and reserve price are determined by the lower end of the corresponding shutdown curve.Auctions Design; Ex Post Efficiency; Endogenous Participation; Multidimensional Screening; Vickrey Auction

The Economics of Internet Markets

The internet has facilitated the creation of new markets characterized by large scale, increased customization, rapid innovation and the collection and use of detailed consumer and market data. I describe these changes and some of the economic theory that has been useful for thinking about online advertising markets, retail and business-to-business e-commerce, internet job matching and financial exchanges, and other internet platforms. I also discuss the empirical evidence on competition and consumer behavior in internet markets and some directions for future research.internet, market, innovation, advertising, retail, e-commerce, financial exchanges