Affiliated Private Values Research Articles

Robust auctions with affiliated private values

Robust auctions with affiliated private values

Semi-nonparametric estimation of secret reserve prices in auctions

This letter proposes an estimation method for the distribution of unobservable secret seller reserve prices in auctions. Within the symmetric affiliated private values model, I construct a density estimator using the semi-nonparametric quasi maximum likelihood approach developed by Gallant and Nychka (1987). I then use Monte Carlo experiments to demonstrate its performance in relatively small samples. A discussion on applying this method to structurally similar identification problems is provided. • This letter offers an approach to identify the distribution of secret reserve prices. • The model allows for affiliated private values among buyers and sellers. • Input data include the auction’s paying bid and whether the item sold at said bid. • A semi-nonparametric estimator identifies the distribution of secret reserve prices. • This method works well in relatively small samples ( ∼ 100 ).

Nonparametric identification and estimation of all-pay auction and contest models

AbstractIn this paper, I study the nonparametric identification and estimation of multi-unit all-pay auctions of incomplete information. First, I consider the setting where multiple goods are allocated among several risk-neutral participants with independent private values (IPV). I prove the nonparametric identification of the model and derive two different consistent estimators of the distribution of bidder valuations. The first estimator is based on the classical structural approach similar to that of Guerre et al. (Econometrica 68(3):525–574, 2000). The second estimator, instead, allows estimation of the quantile function of the bidders’ valuations directly using the quantile density of the bids. Monte Carlo simulations show good small sample property under various assumptions of the number of players and goods. Next, I consider a variety of model extensions: the case of affiliated private values (APV), asymmetric players, the addition of random noise, as well as the case of risk-averse bidders. In contrast to all other scenarios, I prove that the general model with risk-averse bidders is not identified even in the semi-parametric case in which utility function is restricted to belong to the class of functions with constant absolute risk aversion (CARA). On the other hand, I show that the model with risk aversion can be identified if the distribution of valuations is restricted to having fixed support.

Instrumental variables estimation of a simple dynamic model of bidding behavior in private value auctions

We provide the first, in experimental economics, consistent estimates of a dynamic learning model with a continuous outcome. The econometric approach we propose can be used in many experimental studies including auctions, bargaining with transfers, and gift exchange experiments. We focus on affiliated private value auctions, where subjects are generally assumed to converge to the rule-of-thumb bidding, but our general approach is applicable to many other settings. Our IV estimates suggest that subjects become significantly less aggressive over time; specifically, they decrease their bids in proportion to the previous period’s signal minus bid. However, the inconsistent OLS and FE estimators imply that subjects become significantly more aggressive over time—they raise their bids in proportion to the previous period’s signal minus bid. Our instruments are randomly generated by the experiment, and pass popular weak instrument tests.

Urban Environmental Evaluation Using Affiliated Private Value Auction Model

This study evaluates the policy that brings non-marginal changes in an urban environmental attribute, fire risk, by using real estate auction data. Our evaluation is based on the extrapolation of the value distribution for auctioned real estate. In the estimation, we propose a simulated method of moments that is based on the moment conditions on order statistics of bids. We consider the possibility of affiliation by applying the Archimedean copula. Our estimation result rejects the hypothesis that bidders' valuation for apartments is independent when we assume that the marginal distribution of value follows log-normal or exponential distributions.

All-pay auctions with affiliated binary signals

We analyze all-pay auctions with affiliated values and binary signals. We analyze the unique symmetric equilibrium with any number of bidders and show that the bidders earn positive rents only if the equilibrium is monotone. We also characterize the symmetric equilibrium of the closely related two-player war of attrition.We compare expected revenues across these formats. All-pay auctions result in lower expected rents to the bidders than standard auctions, but they also induce inefficient allocations in some models with affiliated private values. With two bidders, the effect on rent extraction dominates, and the all-pay auctions outperform standard auctions in terms of expected revenue. With many bidders, standard auctions may result in higher expected revenue. The war of attrition outperforms the standard auctions in terms of revenue, but its ranking relative to all-pay auctions is ambiguous.

War of Attrition with Affiliated Values

We study the war of attrition between two players when the players’ signals are binary and affiliated. Our model covers both the case of common values and affiliated private values. We characterize the unique symmetric equilibrium and demonstrate the possibility of nonmonotonic symmetric equilibria, i.e. equilibria where the player with a lower signal wins with positive probability. Such an outcome is inefficient in the case of private valuations. We compare the war of attrition to other related mechanisms, the all-pay auction and standard first and second-price auctions. The war of attrition dissipates the bidders’ rents more effectively but at the same time distorts the allocation more severely than the other mechanisms. In terms of expected revenues, the war of attrition dominates the standard auctions, but the ranking against the all-pay auction is ambiguous.

All-Pay Auctions with Affiliated Values

This paper analyzes all-pay auctions where the bidders have affiliated values for the object for sale and where the signals take binary values. Since signals are correlated, high signals indicate a high degree of competition in the auction and since even losing bidders must pay their bid, non-monotonic equilibria arise. We show that the game has a unique symmetric equilibrium, and that whenever the equilibrium is non-monotonic the contestants earn no rents. All-pay auctions result in low expected rents to the bidders, but also induce inefficient allocations in models with affiliated private values. With two bidders, the effect on rent extraction dominates, and all-pay auction outperforms standard auctions in terms of expected revenue. With many bidders, this revenue ranking is reversed for some parameter values and the inefficient allocations persist even in large auctions.

Affiliation and Entry in First-Price Auctions with Heterogeneous Bidders: An Analysis of Merger Effects

We study the effects of mergers in timber sale auctions in Oregon. We propose an entry and bidding model within the affiliated private value (APV) framework and with heterogeneous bidders, and establish existence of the entry equilibrium and existence and uniqueness of the bidding equilibrium when the joint distribution of private values belongs to the class of Archimedean copulas. We estimate the resulting structural model, and study merger effects through counterfactual analyses using the structural estimates. We evaluate how merger effects depend on affiliation, entry, and the auction mechanism and find that the seller may benefit from some mergers. (JEL C57, D44, G34, L11, L73)

Small business set-asides in procurement auctions: An empirical analysis

As part of public procurement, many governments adopt small business programs to provide contract opportunities for businesses often with preferences for firms operated by members of groups designated as disadvantaged. The redistribution arising from such programs, however, can introduce significant additional costs to government procurement budgets. In this paper, the extent to which small business set-asides increased government procurement costs is examined. The estimates employ data on Japanese public construction projects, where approximately half of the procurement budget is set aside for small and medium enterprises (SMEs). Applying a positive relationship between profitability and firm size obtained by the nonparametric estimation of an asymmetric first-price auction model with affiliated private values, a counterfactual analysis is undertaken to demonstrate that approximately 40percent of SMEs would exit the procurement market if set-asides were removed. Surprisingly, the resulting lack of competition would increase government procurement costs more than it would offset the production cost inefficiency.

Competition May Reduce the Revenue in a First Price Auction with Affiliated Private Values

There is a widespread belief that in auctions with private values, the seller's revenue is increasing in the number of bidders. We show that there exists an auction setting with symmetric and affiliated private values in which the seller's expected revenue in a first price auction is decreasing in the number of bidders who participate in the auction.

Nonparametric Identification of Risk Aversion in First-Price Auctions Under Exclusion Restrictions

This paper studies the nonparametric identification of the first-price auction model with risk averse bidders within the private value paradigm. First, we show that the benchmark model is nonindentified from observed bids. We also derive the restrictions imposed by the model on observables and show that these restrictions are weak. Second, we establish the nonparametric identification of the bidders' utility function under exclusion restrictions. Our primary exclusion restriction takes the form of an exogenous bidders' participation, leading to a latent distribution of private values that is independent of the number of bidders. The key idea is to exploit the property that the bid distribution varies with the number of bidders while the private value distribution does not. We then extend these results to endogenous bidders' participation when the exclusion restriction takes the form of instruments that do not affect the bidders' private value distribution. Though derived for a benchmark model, our results extend to more general cases such as a binding reserve price, affiliated private values, and asymmetric bidders. Last, possible estimation methods are proposed.

Bidding rings and the winner's curse

This article extends the theory of legal cartels to affiliated private value and common value environments. We show that efficient collusion is always possible in private value environments, but may not be in common value environments with a binding reserve price. In the latter case, collusion does more than simply transfer rents from the seller to the buyers, it also gives buyers a chance to pool their information prior to trade and make an efficient investment decision. However, full efficiency may not be compatible with information revelation. Buyers with high signals may be better off if no one colludes, leading to inefficient trade. This result provides a possible explanation for the low incidence of joint bidding, especially on marginal tracts, in U.S. federal government offshore oil and gas lease auctions.

Unobserved correlation in private-value ascending auctions

In private-value ascending auctions, the winner's willingness to pay is not observed, leading to underidentification of many econometric models. I calculate tight bounds on expected revenue and optimal reserve price for the case of symmetric and affiliated private values.

Hybrid auctions revisited

We examine hybrid auctions with affiliated private values and risk-averse bidders, and show that the optimal hybrid auction trades off the benefit of information extraction in the ascending-bid phase and the cost of reduced competition in the sealed-bid phase.

Equilibrium in the two-player, [formula omitted]-double auction with affiliated private values

We present sufficient conditions for the existence of an increasing equilibrium in the two-player, k-double auction with affiliated private values. In the case k ∈ { 0 , 1 } there exists a unique equilibrium in non-dominated strategies. Applying this equilibrium, we provide a detailed example illustrating how dependence level affects strategic bidding. In the case k ∈ ( 0 , 1 ) we prove existence of a continuum of strictly increasing equilibria, and illustrate them using an example. Furthermore, we show that equilibria in the case of independent private values are pointwise limits of equilibria with strictly affiliated private values.

Equilibrium in the Two Player, k-Double Auction with Affiliated Private Values

We present sufficient conditions for the existence of an increasing equilibrium in the two player k-double auction with affiliated private values. In the case k ∈ {0, 1} there exists a unique equilibrium in non-dominated strategies. Applying this equilibrium, we provide a detailed example illustrating how dependence level affects strategic bidding. In the case k ∈ (0, 1) we prove existence of a continuum of strictly increasing equilibria, and illustrate them using an example. Furthermore, we show that equilibria in the case of independent private values are pointwise limits of equilibria with strictly affiliated private values.

Nonparametric estimation of asymmetric first price auctions: A simplified approach

We present an approach to nonparametric estimation of pseudo-values in asymmetric affiliated private values (APV) models for first price auctions that eliminates the ‘curse of dimensionality.’ We show that pseudo-values can be estimated by using two-dimensional functions of bids for APV models regardless of the form of asymmetry.

Maximizing earnings and price fairness perceptions in online consumer-to-consumer auctions

We examine the effects of starting bids on seller earnings in online consumer-to-consumer auctions. As starting bids increase, and the number of bidders increase, seller earnings increase. Both the affiliated private value model and a reference price explanation explain seller earnings. Bidder price fairness perceptions are also evaluated and, higher starting bids positively impact price fairness perceptions for winning bidders but have an adverse effect on losing bidders. In total, these findings suggest that sellers receive greater earnings as well as no adverse price fairness perceptions from winning bidders by setting starting bids higher.

Asymmetry in first‐price auctions with affiliated private values

AbstractCollusion and heterogeneity across firms may introduce asymmetry in bidding games. A major difficulty in asymmetric auctions is that the Bayesian Nash equilibrium strategies are solutions of an intractable system of differential equations. We propose a simple method for estimating asymmetric first‐price auctions with affiliated private values. Considering two types of bidders, we show that these differential equations can be rewritten using the observed bid distribution. We establish the identification of the model, characterize its theoretical restrictions, and propose a two‐step non‐parametric estimation procedure for estimating the private value distributions. An empirical analysis of joint bidding in OCS auctions is provided. Copyright © 2003 John Wiley & Sons, Ltd.