Auctions with Variable Supply: Uniform Price versus Discriminatory

We examine an auction in which the seller determines the supply after observing the bids. We compare the uniform price and the discriminatory auction in a setting of supply uncertainty. Uncertainty is caused by the interplay of two factors: the seller's private information about marginal cost, and the seller's incentive to sell the profit-maximizing quantity given the received bids. In every symmetric mixed strategy equilibrium, bidders submit higher bids in the uniform price auction than in the discriminatory auction. In the two-bidder case this result extends to the set of rationalizable strategies. As a consequence, we find that the uniform price auction generates higher expected revenue for the seller and higher trade volume.sealed bid multi-unit auctions, variable supply auctions, discriminatory and uniform price auctions, subgame perfect equilibria, rationalizable strategies

Econometrics for Learning Agents

The main goal of this paper is to develop a theory of inference of player valuations from observed data in the generalized second price auction without relying on the Nash equilibrium assumption. Existing work in Economics on inferring agent values from data relies on the assumption that all participant strategies are best responses of the observed play of other players, i.e. they constitute a Nash equilibrium. In this paper, we show how to perform inference relying on a weaker assumption instead: assuming that players are using some form of no-regret learning. Learning outcomes emerged in recent years as an attractive alternative to Nash equilibrium in analyzing game outcomes, modeling players who haven't reached a stable equilibrium, but rather use algorithmic learning, aiming to learn the best way to play from previous observations. In this paper we show how to infer values of players who use algorithmic learning strategies. Such inference is an important first step before we move to testing any learning theoretic behavioral model on auction data. We apply our techniques to a dataset from Microsoft's sponsored search ad auction system

Uniform vs. Discriminatory Auctions with Variable Supply - Experimental Evidence

In the variable supply auction considered here, the seller decides how many costumers with unit demand to serve after observing their bids. Bidders are uncertain about the seller's cost. We experimentally investigate whether a uniform or a discriminatory price auction is better for the seller in this setting. Exactly as predicted by theory, it turns out that the uniform price auction produces substantially higher bids, and consequently yields higher revenues and profits for the seller. Somewhat surprisingly but again predicted by theory, it also yields a higher number of transactions, which makes it the more efficient auction format.auctions, experiment, discriminatory, uniform

Uniform vs. Discriminatory Auctions with Variable Supply - Experimental Evidence

In the variable supply auction considered here, the seller decides how many costumers with unit demand to serve after observing their bids. Bidders are uncertain about the seller's cost. We experimentally investigate whether a uniform or a discriminatory price auction is better for the seller in this setting. Exactly as predicted by theory, it turns out that the uniform price auction produces substantially higher bids, and consequently yields higher revenues and profits for the seller. Somewhat surprisingly but again predicted by theory, it also yields a higher number of transactions, which makes it the more efficient auction format.

Information in Mechanism Design

We survey the recent literature on the role of information in mechanism design. First, we discuss an emerging literature on the role of endogenous payoff and strategic information for the design and the efficiency of the mechanism. We specifically consider information management in the form of acquisition of new information or disclosure of existing information. Second, we argue that in the presence of endogenous information, the robustness of the mechanism to the type space and higher order beliefs becomes a natural desideratum. We discuss recent approaches to robust mechanism design and robust implementation.Mechanism Design, Information Acquisition, Ex Post Equilibrium, Robust Mechanism Design, Interdependent Values, Information Management

On Rationalizable Outcomes in Private-Value First-Price Discrete Auctions

In this paper, we extend the result of Dekel and Wollinsky ("Rationalizable Outcomes of Large Private-Value First-Price Discrete Auctions" Games and Economic Behavior, 2003) on rationalizable outcomes in first-price auctions. Dekel and Wollinsky show that under certain conditions, each player chooses a unique bid conditional on her valuation. Their result however depends on the assumption that the number of players is sufficiently large (relative to the number of available bids). We first provide a different set of sufficient conditions for the uniqueness result. We then show that for the independent (possibly asymmetric) private value case, (i) the result holds if the distributions are such that the inverse hazard rate is sufficiently high for each valuation, implying that auctions need not necessarily be large, and (ii) if the distributions satisfy the conditions of Dekel and Wollinsky, they always satisfy oursFirst-Price Auctions, Rationalizability, Dominance

Uniform vs. discriminatory auctions with variable supply : experimental evidence

In the variable supply auction considered here, the seller decides how many costumers with unit demand to serve after observing their bids. Bidders are uncertain about the seller's cost. We experimentally investigate whether a uniform or a discriminatory price auction is better for the seller in this setting. Exactly as predicted by theory, it turns out that the uniform price auction produces substantially higher bids, and consequently yields higher revenues and profits for the seller. Somewhat surprisingly but again predicted by theory, it also yields a higher number of transactions, which makes it the more efficient auction format

Dominance-Solvable Lattice Games

This paper derives sufficient and necessary conditions for dominance-solvability of so-called lattice games whose strategy sets have a lattice structure while they simultaneously belong to some metric space. The argument combines and extends Moulin's (1984) approach for nice games and Milgrom and Roberts' (1990) approach for supermodular games. The analysis covers - but is not restricted to - the case of actions being strategic complements as well as the case of actions being strategic substitutes. Applications are given for n-firm Cournot oligopolies, auctions with bidders who are optimistic - respectively pessimistic - with respect to an imperfectly known allocation rule, and Two-player Bayesian models of bank runs.