Independent Private Values Research Articles

Does jump bidding increase sellers’ revenue? Theory and experiment

We consider an environment in which bidders decide whether to jump bids in a simple two-bidder ascending auction with independent private values. We compare two types of equilibria, one that involves jump bidding and another that does not. We show that the revenue in the jump bidding equilibrium dominates that in the no-jump equilibrium when bidders are risk averse. Isolating the revenue impact of jump bidding from that of overbidding, our experimental design allows us to demonstrate that sellers’ revenue increases due to jump bidding but only insignificantly so.

Testing for risk aversion in first-price sealed-bid auctions

We consider testing for risk aversion in first-price sealed-bid auctions with symmetric bidders and independent private values. We impose several restrictions on the parameter space, which are all implied by Guerre et al. (2009)’s exclusion restriction, and we articulate what restrictions are needed for our test to control the limiting size and to be pointwise consistent. Critical values can be obtained from the standard normal distribution. We also analyze local-power properties and show that our test detects local alternative at the parametric rate.

Revealing information in auctions: The optimal auction versus the second-price auction

We study the optimal information disclosure policy in the optimal auction and the second-price auction when the seller has information that additively adjusts the independent private values of the bidders. In this setting, information revelation could change the allocation of the good in both types of auctions. However, in the optimal auction, the change in allocation makes the revenue function convex in the additive adjustments, so the seller should always reveal information. In contrast, in the second-price auction, the change in allocation makes the revenue function non-convex, in which case the seller might benefit from withholding information.

Semiparametric Quantile Models for Ascending Auctions With Asymmetric Bidders

The article proposes a parsimonious and flexible semiparametric quantile regression specification for asymmetric bidders within the independent private value framework. Asymmetry is parameterized using powers of a parent private value distribution, which is generated by a quantile regression specification. As noted in Cantillon, this covers and extends models used for efficient collusion, joint bidding and mergers among homogeneous bidders. The specification can be estimated for ascending auctions using the winning bids and the winner’s identity. The estimation is in two stage. The asymmetry parameters are estimated from the winner’s identity using a simple maximum likelihood procedure. The parent quantile regression specification can be estimated using simple modifications of Gimenes. Specification testing procedures are also considered. A timber application reveals that weaker bidders have 30% less chances to win the auction than stronger ones. It is also found that increasing participation in an asymmetric ascending auction may not be as beneficial as using an optimal reserve price as would have been expected from a result of Bulow and Klemperer valid under symmetry.

How Managed Entry Agreements can improve allocation in the public health system: a mechanism design approach.

The process of introducing a new health technology into a healthcare system is characterized by uncertainty and risk for those involved-pharmaceutical companies, payers, patients and the government. In view of the accelerated introduction of new technologies in recent years, mechanisms to reduce uncertainty are of growing interest. One example is the Managed Entry Agreement (MEA), which we explore using a mechanism design approach. We make use of the Israeli experience, in which pharmaceutical companies and health plans (i.e., payers) negotiate over the introduction of new technologies into the national Health Services Basket (HSB) with the Ministry of Health acting as a mediator. We use the framework of bargaining within a mechanism design framework to show that in the process of negotiation the parties, the pharmaceutical company (PC) and the health plan (HP), have independent private valuations and that a situation of common knowledge that gains from MEA exists is rare. Adding a mediator (i.e., the MEA team) to the mechanism, as in a direct-revelation mechanism, reduces the level of uncertainty for both sides (i.e., the PC and the HP), thus making it possible to meet the budget constraint while increasing value for patients and enhancing ex-post efficiency.

The optimal sequence of prices and auctions

To sell a good before a deadline, a monopolist chooses between posting a price and running a costly reserve-price auction each period. Buyers with independent private values arrive over time. For a wide range of auction costs, the profit-maximizing mechanism sequence is to post prices first and then to run auctions. The optimality of the prices-then-auctions mechanism sequence provides a new justification for the hybrid sales mechanism of allowing the “Buy It Now” option before a standard auction on eBay.

All-pay auctions with private signals about opponents’ values

We study all-pay auctions where each player observes her private value as well as a noisy private signal about the opponent’s value, following Fang and Morris’s (J Econ Theory 126(1):1–30, 2006) analysis of winner-pay auctions with multidimensional private signals. A unique symmetric monotonic equilibrium exists if the signal is not informative enough. When the signal is sufficiently informative, there exists a symmetric non-monotonic equilibrium in which all types of players randomize in overlapping supports. The revenue is lower than that in the standard independent private value setting. Fixing the signal’s informativeness, the all-pay auction raises lower revenue than the second-price auction, whereas the revenue ranking between the all-pay and the first-price auction is ambiguous.

Optimal Auction Design in a Common Value Model

We study auction design when bidders have a pure common value equal to the maximum of their independent signals. In the revenue maximizing mechanism, each bidder makes a payment that is independent of his signal and the allocation discriminates in favor of bidders with lower signals. We provide a necessary and sufficient condition under which the optimal mechanism reduces to a posted price under which all bidders are equally likely to get the good. This model of pure common values can equivalently be interpreted as model of resale: the bidders have independent private values at the auction stage, and the winner of the auction can make a take-it-or-leave-it-offer in the secondary market under complete information.

Sample Spacings for Identification: The Case of English Auctions With Absentee Bidding

This paper presents new nonparametric identification results for ascending auctions with independent private values. The standard identification approach is infeasible in the motivating setting, because absentee bidding conceals the number of bidders. I exploit insights from the statistics literature about the stochastic ordering of adjacent sample spacings. I show how to use such sample spacings to set-identify structural features, using an incomplete model and without knowing all highest bids or the number of bidders. Applying the sample spacing method to a small sample of wine auctions, I show that it identifies informative bounds on policy-relevant counterfactuals. It turns out that Sotheby's restricts full exploitation of the exclusion principle of optimal reserve prices. As a result, sellers set sub-optimally low reserve prices. They benefit up to 13% from adopting a common reserve price rule equal to 120% of the Wine Department's pre-auction value estimate.

Optimal monotone signals in Bayesian persuasion mechanisms

This paper develops a new approach—based on the majorization theory—to the information design problem in Bayesian persuasion mechanisms, i.e., models in which the sender selects the signal structure of the agent(s) who then reports it to the non-strategic receiver. We consider a class of mechanisms in which the posterior payoff of the sender depends on the value of a realized posterior mean of the state, its order in the sequence of possible means, and the marginal distribution of signals. We provide a simple characterization of mechanisms in which optimal signal structures are monotone partitional. Our approach has two economic implications: it is invariant to monotone transformations of the state and allows to decompose setups with multiple agents into independent Bayesian persuasion mechanisms with a single agent. As the main application of our characterization, we show the optimality of monotone partitional signal structures in all selling mechanisms with independent private values and quasi-linear preferences. We also provide sharp characterization of optimal signal structures for second-price auctions and posted-price sales.

Optimal reserve prices in sealed-bid auctions with reference effects

The reference effect and loss aversion are incorporated into the buyer’s utility in the symmetric independent private value models of sealed-bid auctions. The buyer’s equilibrium bidding strategy and the seller’s optimal reserve price are derived for the first-price and second-price sealed-bid auctions. In both auction mechanisms, the seller’s optimal reserve price and expected revenue are increasing in the reference point. We compare the seller’s expected revenues as well as the optimal reserve prices in the two auctions. The results show that the seller will set a higher optimal reserve price but obtain lower optimal expected revenue in the second-price auction compared to the first-price auction. Further, we extend the model to the gain-seeking case, and endogenize the reference point as the ex-ante expected price of the item in equilibrium. In contrast to the loss-averse case, the seller will set a lower optimal reserve price but obtain higher optimal expected revenue in the second-price auction compared to the first-price auction if the buyers are gain-seeking. With an endogenous reference point, similar results are obtained in terms of revenue comparison between the two auctions.

Robust bidding and revenue in descending price auctions

We study the properties of Dutch auctions in an independent private value setting, where bidders face uncertainty over the type distribution of their opponents and evaluate their payoffs by the worst case from a set of probabilistic scenarios. In contrast to static auction formats, participants in the Dutch auction gradually learn about the valuations of other bidders. We show that the transmitted information can lead to changes in the worst-case distribution and thereby shift a bidder's payoff maximizing exit price over time. We characterise the equilibrium bidding function in this environment and show that the arriving information leads bidders to exit earlier at higher prices. As a result, the Dutch auction systematically generates more revenue than the first-price auction.

Value-Rationalizability in Auction Bidding

In a symmetric first-price or second-price auction, a bidding strategy is characterized as value-rationalizable if it can be viewed as being realized at a Nash equilibrium under the specification of a non-negative and increasing value function. In an environment where the underlying probabilistic framework is common knowledge, we investigate conditions for value-rationalizability by examining the value functions, which are induced by a bidding strategy. The existence of value-rationalizable strategies with infinite large induced functions is established. We argue that an improper specification of the value function should be attributed to bounded rationality. We show that, under assumptions, strategies which are not value-rationalizable are sub-optimal responses. Finally, the degree of irrationality is assessed by measuring the deviation of the induced function from being a proper value function in terms of its sign and monotonicity. The findings are illustrated by different examples in the independent private value paradigm and the interdependent value setting.

Informationally Simple Implementation

We consider a mechanism design setting in which agents can acquire costly information on their preferences as well as others’. The choice of the mechanism generates informational incentives as it affects what information is acquired before play begins. A mechanism is informationally simple if agents have no incentive to learn about others’ preferences. This property is of interest for two reasons: First, the extended game has an equilibrium in dominant strategies only if it is informationally simple. Second, this endogenizes an independent private value property of the interim information structure. Our main result is that a mechanism is informationally simple only if it is de facto dictatorial. This holds for generic environments and any smooth cost function which satisfies an Inada condition. Hence even interim strategy-proof mechanisms incentivize agents to learn about others, and do not admit dominant strategies at the ex-ante stage. Moreover, the Independent Private Value assumption is unlikely to arise endogenously, though we show that full surplus extraction is infeasible.

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 iscredibleif 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.

Bidding collusion without passive updating

Collusion here takes the form of a side transfer between two bidders proposed by a mediator, before a first-price auction with independent private values. I find a necessary and sufficient condition, in terms of the bidders’ prior distributions, for existence of a side transfer acceptable to all types of both bidders on path of a perfect Bayesian equilibrium. The class of distributions defined by this condition is larger than the class under the passive updating assumption in the mechanism design literature on collusion. The off-path posterior belief most conducive to collusion entails a continuation equilibrium as if the collusion vetoer were bidding against a naive, value-bidding rival.

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.

Nash Equilibria for a Quadratic Voting Game

A group of N individuals must choose between two collective alternatives. Under Quadratic Voting (QV), agents buy votes in favor of their preferred alternative from a clearing house, paying the square of the number of votes purchased; the sum of all votes purchased determines the outcome. We provide the first rigorous results for this mechanism, in a canonical independent private values environment with bounded value distributions. In addition to characterizing the nature of equilibria, we demonstrate that for all bounded value distributions, the utilitarian welfare losses of the mechanism as a proportion of the maximum possible welfare tends to zero as the population size becomes large.

Unique equilibrium in contests with incomplete information

Considered are imperfectly discriminating contests in which players may possess private information about the primitives of the game, such as the contest technology, valuations of the prize, cost functions, and budget constraints. We find general conditions under which a given contest of incomplete information admits a unique pure-strategy Nash equilibrium. In particular, provided that all players have positive budgets in all states of the world, existence requires only the usual concavity and convexity assumptions. Information structures that satisfy our conditions for uniqueness include independent private valuations, correlated private values, pure common values, and examples of interdependent valuations. The results allow dealing with inactive types, asymmetric equilibria, population uncertainty, and the possibility of resale. It is also shown that any player that is active with positive probability ends up with a positive net rent.

Inference for first-price auctions with Guerre, Perrigne, and Vuong’s estimator

We consider inference on the probability density of valuations in the first-price sealed-bid auctions model within the independent private value paradigm. We show the asymptotic normality of the two-step nonparametric estimator of Guerre et al. (2000) (GPV), and propose an easily implementable and consistent estimator of the asymptotic variance. We prove the validity of the pointwise percentile bootstrap confidence intervals based on the GPV estimator. Lastly, we use the intermediate Gaussian approximation approach to construct bootstrap-based asymptotically valid uniform confidence bands for the density of the valuations.