Credible Auctions: A Trilemma

Consider an extensive‐form mechanism, run by an auctioneer who communicates sequentially and privately with bidders. Suppose the auctioneer can deviate from the rules provided that no single bidder detects the deviation. A mechanism is credible if it is incentive‐compatible for the auctioneer to follow the rules. We study the optimal auctions in which only winners pay, under symmetric independent private values. The first‐price auction is the unique credible static mechanism. The ascending auction is the unique credible strategy‐proof mechanism.

Soft Floors in Auctions

Several of the auction-driven exchanges that facilitate programmatic buying of internet display advertising have recently introduced “soft floors” in addition to standard reserve prices (called “hard floors” in the industry). A soft floor is a bid level below which a winning bidder pays his own bid instead of paying the second-highest bid as in a second-price auction most ad exchanges use by default. This paper characterizes soft floors’ revenue-generating potential as a function of the distribution of bidder independent private values. When bidders are symmetric (identically distributed), soft floors have no effect on revenue, because a symmetric equilibrium always exists in strictly monotonic bidding strategies, and standard revenue-equivalence arguments thus apply. The industry often motivates soft floors as tools for extracting additional expected revenue from an occasional high bidder, for example a bidder retargeting the consumer making the impression. Such asymmetries in the distribution of bidder preferences do not automatically make soft floors profitable. This paper presents two examples of tractable modeling assumptions about such occasional high bidders, with one example implying low soft floors always hurt revenues because of strategic bid-shading by the regular bidders, and the other example implying high soft floors can increase revenues by making the regular bidders bid more aggressively. This paper was accepted by Juanjuan Zhang, marketing.

Linear Voting Rules

How should a society choose between two social alternatives if participation in the decision process is voluntary and costly, and monetary transfers are not feasible? Assuming symmetric independent private values, we show that it is utilitarian‐optimal to use a linear voting rule: votes get alternative‐dependent weights, and a default obtains if the weighted sum of votes stays below some threshold. Any combination of weights and threshold can be optimal. A standard quorum rule can be optimal only when it yields the same outcome as a linear rule. A linear rule is called upper linear if the default is upset at every election result that meets the threshold exactly. We develop a perturbation method to characterize equilibria of voting rules in the case of small participation costs and show that leaving participation voluntary increases welfare for any two‐sided upper linear rule that is optimal under compulsory participation.

Entry Deterrence in Dynamic Second-Price Auctions

We examine a dynamic second-price auction with independent private values and sequential costly entry. We show that delayed revelation equilibria exist in which some buyers place coordinated low early bids. These buyers revise their bids to reflect their true valuations just prior to the end of the auction. Compared to the benchmark immediate revelation equilibrium, in which buyers bid their valuations immediately after entry, fewer high-value bidders enter on expectation in the delayed revelation equilibria. Delayed revelation of buyer values decreases social welfare, but is necessary for bidders to have a strict participation incentive. (JEL D44, D82, D83)

Comparative Evaluation of Independent Private Values Distributions on Internet Auction Performance

The Independent Private Values (IPV) model is foundational for the analysis of Internet auction performance and is widely used in the study of auction behaviour. The characteristics of this model include the assumptions of privacy and independence where the value of the commodity in question is private to the individual buyers, and that different buyers do not know the values other buyers attached to the commodity. In addition, these values are drawn from a common distribution which is known to the buyers. In probabilistic terms, this essentially amounts to a series of values which are independent and identically distributed. The features and characteristics of the IPV distribution will have a significant impact on auction behaviour, and since a general stochastic analysis of their impact is analytically intractable, here auction performance is studied using an auction process simulator. Both hard close and soft close Internet auctions are studied. In addition, Vickrey auctions and auction mechanisms with multiple bid acceptance are compared and evaluated. From experimental findings, the paper establishes quantitative relationships between the different auction process parameters, deploy suitable IPV distributions to model the characteristics of different communities of bidders, provide suggestions for optimising auction performance, and recommend strategies for efficient auction design.

UNIFORM BIAS STUDY AND BAHADUR REPRESENTATION FOR LOCAL POLYNOMIAL ESTIMATORS OF THE CONDITIONAL QUANTILE FUNCTION

This paper investigates the bias and the weak Bahadur representation of a local polynomial estimator of the conditional quantile function and its derivatives. The bias and Bahadur remainder term are studied uniformly with respect to the quantile level, the covariates, and the smoothing parameter. The order of the local polynomial estimator can be higher than the differentiability order of the conditional quantile function. Applications of the results deal with global optimal consistency rates of the local polynomial quantile estimator, performance of random bandwidths, and estimation of the conditional quantile density function. The latter allows us to obtain a simple estimator of the conditional quantile function of the private values in a first-price sealed bids auction under the independent private values paradigm and risk neutrality.