For-Profit Search Platforms

We consider optimal pricing by a profit-maximizing platform running a dynamic search and matching market. Buyers and sellers enter in cohorts over time, meet and bargain under private information. The optimal centralized mechanism, which involves posting a bid-ask spread, can be decentralized through participation fees charged by the intermediary to both sides. The sum of buyers’ and sellers’ fees equals the sum of inverse hazard rates of the marginal types and their ratio equals the ratio of buyers’ and sellers’ bargaining weights. We also show that a monopolistic intermediary in a search market may be welfare enhancing

Convergence of a Dynamic Matching and Bargaining Market with Two-sided Incomplete Information to Perfect Competition

Consider a decentralized, dynamic market with an infinite horizon in which both buyers and sellers have private information concerning their values for the indivisible traded good. Time is discrete, each period has length ä, and each unit of time a large number of new buyers and sellers enter the market to trade. Within a period each buyer is matched with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, both the seller and winning buyer exit the market with their realized utility. Traders who fail to trade either continue in the market to be rematched or become discouraged with probability äµ (µ is the discouragement rate) and exit with zero utility. We characterize the steady-state, perfect Bayesian equilibria as ä becomes small and the market–in effect– becomes large. We show that, as ä converges to zero, equilibrium prices at which trades occur converge to the Walrasian price and the realized allocations converge to the competitive allocation.

Quantile-Based Nonparametric Inference for First-Price Auctions

We propose a quantile-based nonparametric approach to inference on the probability density function (PDF) of the private values in first-price sealed-bid auctions with independent private values. Our method of inference is based on a fully nonparametric kernel-based estimator of the quantiles and PDF of observable bids. Our estimator attains the optimal rate of Guerre, Perrigne, and Vuong (2000), and is also asymptotically normal with the appropriate choice of the bandwidth. As an application, we consider the problem of inference on the optimal reserve price.First-price auctions; independent private values; nonparametric estimation; kernel estimation; quantiles; optimal reserve price

Quantile-Based Nonparametric Inference for First-Price Auctions

We propose a quantile-based nonparametric approach to inference on the probability density function (PDF) of the private values in first-price sealed-bid auctions with independent private values. Our method of inference is based on a fully nonparametric kernel-based estimator of the quantiles and PDF of observable bids. Our estimator attains the optimal rate of Guerre, Perrigne, and Vuong (2000), and is also asymptotically normal with the appropriate choice of the bandwidth.First-price auctions; independent private values; nonparametric estimation; kernel estimation; quantiles; optimal reserve price

Supplement to "Quantile-Based Nonparametric Inference for First-Price Auctions"

This paper contains supplemental materials for Marmer and Shneyerov (2010). We discuss here how the approach developed in the aforementioned paper can be applied to conducting inference on the optimal reserve price in first-price auctions, report additional simulations results, and provide a detailed proof of the bootstrap result in Marmer and Shneyerov (2010).First-price auctions, independent private values, nonparametric estimation, kernel estimation, quantiles, optimal reserve price, bootstrap

Convergence of a Dynamic Matching and Bargaining Market with Two-sided Incomplete Information to Perfect Competition

Consider a decentralized, dynamic market with an infinite horizon in which both buyers and sellers have private information concerning their values for the indivisible traded good. Time is discrete, each period has length ?, and each unit of time a large number of new buyers and sellers enter the market to trade. Within a period each buyer is matched with a seller and each seller is matched with zero, one, or more buyers. Every seller runs a first price auction with a reservation price and, if trade occurs, both the seller and winning buyer exit the market with their realized utility. Traders who fail to trade either continue in the market to be rematched or become discouraged with probability ?? (? is the discouragement rate) and exit with zero utility. We characterize the steady-state, perfect Bayesian equilibria as ? becomes small and the market–in effect– becomes large. We show that, as ? converges to zero, equilibrium prices at which trades occur converge to the Walrasian price and the realized allocations converge to the competitive allocation.

How Optimism Leads to Price Discovery and Efficiency in a Dynamic Matching Market

We study a market search equilibrium with aggregate uncertainty, private information and heterogeneus beiefs. Traders initially start out optimistic and then update their beliefs based on their matching experience in the market, using the Bayes rule. It is shown that all separating equilibria converge to perfect competition in the limit as the time between matches tends to 0. We also establish existence of a separating equilibrium.Markets with search frictions, aggregate uncertainty, heterogeneous beliefs, optimism, bargaining, foundations of Walrasian equilibrium

What Model for Entry in First-Price Auctions? A Nonparametric Approach

We develop a nonparametric approach that allows for discrimination among alternative models of entry in first-price auctions. Three models of entry are considered: those of Levin and Smith (1994), Samuelson (1985), and a new model in which the information received at the entry stage is imperfectly correlated with bidder valuations. We derive testable restrictions of these models based on how the pro-competitive selection effect shifts bidder valuation quantiles in response to an increase in the number of potential bidders.First-price auctions, models of entry, selective entry, selection effect, nonparametric estimation, quantiles

Are There Common Values in BC Timber Sales? A Tail-Index Nonparametric Test

We develop a new nonparametric test of common values in first-price auctions and apply it to British Columbia (BC) Timber Sales. The test is based on the behavior of the CDF of bids near the reserve price. We show that the curvature of the CDF is drastically different under private values (PV) and common values (CV). We then show that the problem of discriminating between PV and CV is equivalent to estimating the lower tail index of the bid distribution. Our approach allows for unobserved auction heterogeneity of an arbitrary form, and in particular doesn't require the number of potential bidders to be observable. Drawing on the existing and recent literature on tail index estimation, we characterize the B. Hill (1975) tail index estimator for panels with stochastic dimension and a new semi-parametric estimator of the asymptotic variance for robust inference. For BC Timber Sales, we find overwhelming support for CV.