Searching the eBay Marketplace

This paper proposes a framework for demand estimation with data on bids, bidders' identities, and auction covariates from a sequence of eBay auctions. First the aspect of bidding in a marketplace environment is developed. Form the simple dynamic auction model with IPV and private bidding costs it follows that if participation is optimal the bidder searches with a "reservation bid" for low-price auctions. Extending results from the empirical auction literature and employing a similar two-stage procedure as has recently been used when estimating dynamic games it is shown that bidding costs are non-parametrically identified. The procedure is tried on a new data set. The median cost is estimated at less than 2% of transaction prices.

Searching the eBay Marketplace

This paper proposes a framework for demand estimation with data on bids, bidders' identities, and auction covariates from a sequence of eBay auctions. First the aspect of bidding in a marketplace environment is developed. Form the simple dynamic auction model with IPV and private bidding costs it follows that if participation is optimal the bidder searches with a "reservation bid" for low-price auctions. Extending results from the empirical auction literature and employing a similar two-stage procedure as has recently been used when estimating dynamic games it is shown that bidding costs are non-parametrically identified. The procedure is tried on a new data set. The median cost is estimated at less than 2% of transaction prices

Auctions with Limited Commitment

We study auction design in the standard symmetric independent private values environment, where the seller lacks the commitment power to withhold an unsold object off the market. The seller has a single object and can conduct an infinite sequence of standard auctions with reserve prices to maximize her expected profit. In each period, the seller can commit to a reserve price for the current period but cannot commit to future reserve prices. We analyze the problem with limited commitment through an auxiliary mechanism design problem with full commitment, in which an additional constraint reflects the sequential rationality of the seller. We characterize the maximal profit achievable in any perfect Bayesian equilibrium in the limit as the period length vanishes. The static full commitment profit is not achievable but the seller can always guarantee the profit of an efficient auction. If the number of buyers exceeds a cutoff which is small for many distributions, the efficient auction is optimal. Otherwise, the efficient auction is not optimal, and we give conditions under which the optimal solution consists of an initial auction with a non-trivial reserve price followed by a continuously decreasing price path. The solution is described by a simple ordinary differential equation. Our analysis combines insights from bargaining, auctions, and mechanism design

Rate of Price Discovery in Iterative Combinatorial Auctions

We study a class of iterative combinatorial auctions which can be viewed as subgradient descent methods for the problem of pricing bundles to balance supply and demand. We provide concrete convergence rates for auctions in this class, bounding the number of auction rounds needed to reach clearing prices. Our analysis allows for a variety of pricing schemes, including item, bundle, and polynomial pricing, and the respective convergence rates confirm that more expressive pricing schemes come at the cost of slower convergence. We consider two models of bidder behavior. In the first model, bidders behave stochastically according to a random utility model, which includes standard best-response bidding as a special case. In the second model, bidders behave arbitrarily (even adversarially), and meaningful convergence relies on properly designed activity rules

Using priced options to solve the exposure problem in sequential auctions

We propose a priced options model for solving the exposure problem of bidders with valuation synergies participating in a sequence of online auctions. We consider a setting in which complementary-valued items are offered sequentially by different sellers, who have the choice of either selling their item directly or through a priced option. In our model, the seller fixes the exercise price for this option, and then sells it through a first-price auction. We analyze this model from a decision-theoretic perspective and we show, for a setting where the competition is formed by local bidders (which desire a single item), that using options can increase the expected profit for both sides. Furthermore, we derive the equations that provide minimum and maximum bounds between which the bids of the synergy buyer are expected to fall, in order for both sides of the market to have an incentive to use the options mechanism. Next, we perform an experimental analysis of a market in which multiple synergy buyers are active simultaneously. We show that, despite the extra competition, some synergy buyers may benefit, because sellers are forced to set their exercise prices for options at levels which encourage participation of all buyers.</jats:p

Optimal pricing using online auction experiments: A P\'olya tree approach

We show how a retailer can estimate the optimal price of a new product using observed transaction prices from online second-price auction experiments. For this purpose we propose a Bayesian P\'olya tree approach which, given the limited nature of the data, requires a specially tailored implementation. Avoiding the need for a priori parametric assumptions, the P\'olya tree approach allows for flexible inference of the valuation distribution, leading to more robust estimation of optimal price than competing parametric approaches. In collaboration with an online jewelry retailer, we illustrate how our methodology can be combined with managerial prior knowledge to estimate the profit maximizing price of a new jewelry product.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS503 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Learning Prices for Repeated Auctions with Strategic Buyers

Inspired by real-time ad exchanges for online display advertising, we consider the problem of inferring a buyer's value distribution for a good when the buyer is repeatedly interacting with a seller through a posted-price mechanism. We model the buyer as a strategic agent, whose goal is to maximize her long-term surplus, and we are interested in mechanisms that maximize the seller's long-term revenue. We define the natural notion of strategic regret --- the lost revenue as measured against a truthful (non-strategic) buyer. We present seller algorithms that are no-(strategic)-regret when the buyer discounts her future surplus --- i.e. the buyer prefers showing advertisements to users sooner rather than later. We also give a lower bound on strategic regret that increases as the buyer's discounting weakens and shows, in particular, that any seller algorithm will suffer linear strategic regret if there is no discounting.Comment: Neural Information Processing Systems (NIPS 2013