Optimal auctions with information acquisition

This paper studies optimal auction design in a private value setting with endogenous information gathering. We develop a general framework for modeling information acquisition when a seller wants to sell an object to one of several potential buyers, who can each gather information about their valuations prior to participation in the auction. We first demonstrate that the optimal monopoly price is always lower than the standard monopoly price. We then show that standard auctions with a reserve price remain optimal among symmetric mechanisms, but the optimal reserve price lies between the ex ante mean valuation of bidders and the standard reserve price in Myerson (1981). Finally, we show that the optimal asymmetric mechanism softens the price discrimination against “strong” bidders.     

Competition and confidentiality: Signaling quality in a duopoly when there is universal private information

We model non-cooperative signaling by two firms that compete over a continuum of consumers, assuming each consumer has private information about the intensity of her preferences for the firms' respective products and each firm has private information about its own product's quality. We characterize a symmetric separating equilibrium in which each firm's price reveals its respective product quality. We show that the equilibrium prices, the difference between those prices, the associated outputs, and profits are all increasing functions of the ex ante probability of high safety. If horizontal product differentiation is sufficiently great then equilibrium prices and profits are higher under incomplete information about quality than if quality were commonly known. Thus, while signaling imposes a distortionary loss on a monopolist using price to signal quality, duopolists may benefit from the distortion as it can reduce competition. Finally, average quality is lower since signaling quality redistributes demand towards low-quality firms.     

COGNITIVE EMPATHY IN CONFLICT SITUATIONS

Two individuals are involved in a conflict situation in which preferences are ex ante uncertain. Although they eventually learn their own preferences, they have to pay a small cost if they want to secretly learn their opponent's preferences. We show that there is an interval with an upper bound less than 1 and lower bound greater than zero such that, for sufficiently small positive costs of information acquisition, in any Bayesian Nash equilibrium of the resulting game of incomplete information the probability of acquiring information about the opponent's preferences is within this interval.     

Imperfect Competition in Auction Designs

We study the competition between two owners of identical goods who wish to sell them to a pool of potential buyers. The sellers compete simultaneously setting reserve prices for their second price sealed bid auctions. Upon observing the set reserve prices, the buyers decide simultaneously in which auction to bid. We show that this game has (at least) one equilibrium and that all equilibria are inefficient: reserve prices are not driven to zero (cost). We also discuss where and why the parallel between optimal auction design and optimal pricing in the case of monopoly breaks down for oligopoly.     

An extensive form interpretation of the private core

Summary. The private core of an economy with differential information, (Yannelis (1991)), is the set of all state-wise feasible and private information measurable allocations which cannot be dominated, in terms of ex ante expected utility functions, by state-wise feasible and private information measurable net trades of any coalition. It is coalitionally Bayesian incentive compatible and also takes into account the information superiority of an individual. We provide a noncooperative extensive form interpretation of the private core for three person games. We construct game trees which indicate the sequence of decisions and the information sets, and explain the rules for calculating ex ante expected payoffs. In the spirit of the Nash programme, the private core is thus shown to be supported by the perfect Bayesian equilibrium of a noncooperative game. The discussion contributes not only to the development of ideas but also to the understanding of the dynamics of how coalitionally incentive compatible contracts can be realized. Received: July 21, 2000; revised version: January 16, 2001     

Sequential bargaining,external effects of agreement,and public intervention

In some bargaining situations, agreement has implications for agents beyond the parties involved, and if so, delays in reaching an agreement or failing to reach an agreement, when this would be profitable, may imply significant welfare losses. The question raised in this paper is whether the intervention of a government, who has a positive valuation of agreement and therefore offers a subsidy, will reduce such delays and inabilities to reach agreement? Based on a perfect Bayesian equilibrium in a sequential bargaining game with intervention, we show that in equilibrium intervention always reduces the ex ante equilibrium inefficiency and conditionally reduces expected delays in trade. However, for intervention in the form of a subsidy to take place, the aggregate of the seller’s reservation price and the externalities must be (almost) as high as the buyer’s upper valuation limit.     

Core-stable rings in auctions with independent private values

We propose a semi-cooperative game theoretic approach to check whether a given coalition is stable in a Bayesian game with independent private values. The ex ante expected utilities of coalitions, at an incentive compatible (noncooperative) coalitional equilibrium, describe a (cooperative) partition form game. A coalition is core-stable if the core of a suitable characteristic function, derived from the partition form game, is not empty. As an application, we study collusion in auctions in which the bidders? final utility possibly depends on the winner?s identity. We show that such direct externalities offer a possible explanation for cartels? structures (not) observed in practice.     

Tullock's Puzzle in Pay‐and‐Play Lobbying

We explain Tullock's puzzle of small payments from special interests to policy‐makers by the hold‐up problem between the two parties. We construct a simple lobbying environment where an uninformed policy‐maker is a price‐setter who sells access to two opposed and privately informed lobbyists. The key equilibrium property is “the curse of the ex ante favored lobbyist”; the lobbyist proposing a project with the higher expected public value ends up worse off than the lobbyist proposing a project with the lower expected public value. In the absence of contribution caps, the ex ante favored lobbyist strategically devalues her project, and the resulting competitive devaluations destroy private values, revenues, as well as correlated public values. Ex ante, the policy‐maker benefits from a binding contribution cap protects the ex ante favored lobbyist, eliminates competitive devaluations, and thus remedies the hold‐up problem.     

On the efficiency of ex ante and ex post pricing institutions

Summary This paper compares the performance of three pricing institutions in a decentralized matching model in which random matching occurs. In the first, sellers make public ex ante commitments to trade at pre-specified prices before matching occurs. In the second, the buyer and seller engage in an alternating offer bargaining game once a match has occurred. In the final pricing institution, one party is chosen at random to make a take it or leave it price offer. The steady state equilibrium with ex ante pricing pareto dominates the steady state equilibrium with ex post take it or leave it offers, which in turn pareto dominates the steady state equilibrium with alternating offers. As the discount factor goes to one, the equilibrium with ex ante pricing generates participation rates that tend toward the pareto efficient level. The ex post pricing institutions generate participation rates that are bounded away from efficient levels. The surplus loss associated with switching from ex ante pricing to take it or leave it offers is small when the discount factor is close to one. Contrary to many models of decentralized trade, ex post pricing institutions encourage too much search by buyers.The financial support of the Social Sciences and Humanities Research Council of Canada is gratefully acknowledged. The research for this paper was completed while the author was visiting the University of California at San Diego. The author thanks Douglas Gale for comments.     

Surplus Extraction and Competition

A competitive economy is studied in which sellers offer alternative direct mechanisms to buyers who have correlated private information about their valuations. In contrast to the monopoly case where sellers charge entry fees and extract all buyers' surplus, it is shown that in the unique symmetric equilibrium with competition, sellers hold second price auctions with reserve prices set equal to their cost. Most important, it is a best reply for sellers not to charge entry fees of the kind normally used to extract surplus, even though it is feasible for them to do so.     

Signaling Product Quality by Price

This paper analyzes the role of price as a signal of the quality of a monopoly firm's new product. The quality of the goods is drawn from a continuum and is unknown to consumers. We establish a unique separating equilibrium using equilibrium characterization results for signaling games. The equilibrium price monotonically increases with quality levels and exceeds the complete-information monopoly price for all quality levels but the lowest one. However, the upward distortion decreases as the proportion of pre-informed consumers increases. These results extend both the signaling role of price and characteristics of the separating equilibrium as established in Bagwell and Riordan (1991).     

Alternative theories of wage dispersion

We analyze labor market models where the law of one price fails—i.e., models with equilibrium wage dispersion. We begin considering ex ante heterogeneous workers, but highlight a problem with this approach: If search is costly the market shuts down. We then assume homogeneous workers but ex post heterogeneous matches. This model is robust to search costs, and delivers equilibrium wage dispersion. However, we prove that the law of two prices holds: Equilibrium implies at most two wages. We explore other models, including one combining ex ante and ex post heterogeneity which is robust and delivers more realistic wage dispersion.     

Multiunit Pay‐Your‐Bid Auction with One‐Dimensional Multiunit Demands*

An arbitrary number of units of a good is sold to two bidders through a discriminatory auction. The bidders are homogeneous ex ante and their demand functions are two‐step functions that depend on a single parameter. We characterize the symmetric Bayesian equilibrium and prove its existence and uniqueness. We compare this equilibrium with the equilibrium of the multiunit Vickrey auction and with the equilibria of the single‐unit first price and second price auctions. We examine the consequences of bundling all units into one package. We study the impacts that variations of the “relative” supply have on the equilibrium, on the bidders' average payoffs per unit, and on the efficiency of the equilibrium allocation.     

Information acquisition and welfare effect in a model of competitive financial markets

We analyze welfare effect of information acquisition for a model of competitive financial markets with diverse information and rational expectations. We show that in the fully revealing rational expectations equilibrium, each agent’s gain from trade in ex ante utility decreases as more agents become informed. An implication of the result is that market efficiency and ex ante Pareto optimality are not compatible in competitive financial markets with diverse information and rational expectations. Our result can be viewed as complementary to the Grossman paradox, which shows that market efficiency and individuals’ incentives to acquire information are not compatible. This paper is the first step in a projected exploration of welfare effect of information acquisition in models with diverse information.     

Search less for a better price

In many markets, sellers must spend resources to learn the costs of providing goods/services. This paper considers consumer searches in such markets. The findings show that: (i) even with ex ante identical consumers and sellers, there is price dispersion in the equilibrium, (ii) despite price dispersion and minimal search costs, it could be optimal to search just two sellers and (iii) the optimal number of searches can increase with sellers' information costs.     

Stochastic stability in a double auction

In a k-double auction, a buyer and a seller must simultaneously announce a bid and an ask price respectively. Exchange of the indivisible good takes place if and only if the bid is at least as high as the ask, the trading price being the bid price with probability k and the ask price with probability (1−k). We show that the stable equilibria of a complete information k-double approximate an asymmetric Nash bargaining solution with the seller's bargaining power decreasing in k.Note that ceteris paribus, the payoffs of the seller of the one-shot game increase in k. Nevertheless, as the stochastically stable equilibrium price decreases in k, choosing the seller's favorite price with a relatively higher probability in individual encounters makes him worse off in the long run.     

Incomplete information in rent-seeking contests

We consider a variant of the Tullock lottery contest. Each player’s constant marginal cost of effort is drawn from a potentially different continuous distribution. In order to study the impact of incomplete information, we compare three informational settings to each other; players are either completely informed, privately informed about their own costs, or ignorant of all cost realizations. For the first and the third setting, we determine the unique pure-strategy Nash equilibrium. Under private information, we prove existence of a pure-strategy Bayesian Nash equilibrium and identify a sufficient condition for uniqueness. Assuming that unit cost distributions all have the same mean, we show that under ignorance of all cost realizations ex ante expected aggregate effort is lower than under both private and complete information. Ex ante expected rent dissipation, however, is higher than in the latter settings if we focus on the standard lottery contest and assume costs are all drawn from the same distribution. Between complete and private information, there is neither a general ranking in terms of effort nor in terms of rent dissipation.     

When are stabilizations delayed? Alesina-Drazen revisited

In an influential article, Alesina and Drazen [1991. Why are Stabilizations Delayed? American Economic Review 81, 1170-1188] model delay of stabilization as the result of a struggle between political groups supporting reform plans with different distributional implications. In this paper we show that ex ante asymmetries in the costs of delay for the groups will reduce the probability of conflict and will lead to a shorter expected delay. Accurate common information about the cost of delay may lead to no delay at all. In an asymmetric conflict, a wider divergence in the distributional implications of reform will reduce the probability of conflict but will lead to a longer expected delay. We motivate the asymmetric model of delay by reference to Latin American episodes of the 1980s.     

Oligopolistic Competition and New Technology Adoption under Uncertainty

The paper examines the adoption of a new technology in oligopoly, where there is ex ante uncertainty about variable costs of the new technology. Each firm can either adopt the new process by bearing some up-front investment or may continue to use the old one, after which firms play a Cournot market game. If in equilibrium both technologies are employed, more uncertainty about the new technology increases (decreases) the number of innovating firms and decreases (increases) the product price if the up-front investment is large (small). Our model applies readily to vertical integration if integrated firms neither buy nor sell the intermediate good on the market. However, if buying and selling is allowed, the number of integrated firms is independent of input price uncertainty.     

RETAIL PRICE REGULATION AND THE OPTION TO DELAY

ABSTRACT ** :  This paper examines a two-period model of an investment decision in a network industry characterized by demand uncertainty, economies of scale and sunk costs. In the absence of regulation we identify the market conditions under which a monopolist decides to invest early as well as the underlying overall welfare output. In a regulated environment, we consider a monopolist who faces no downstream (final good) competition but is subject to retail price regulation. We identify the welfare-maximizing regulated prices when the unregulated market outcome is set as the benchmark. We show that if the regulator can commit to ex post regulation – that is, regulated prices that are contingent to future demand realization – then regulated prices that allow the firm to recover its total costs of production are welfare-maximizing. Thus, under ex post price regulation there is no need to compensate the regulated firm for the option to delay that it foregoes when investing today. We argue, however, that regulators cannot make this type of commitment and, therefore, price regulation is often ex ante – that is, regulated prices are not contingent to future demand. We show that the optimal ex ante regulation, and the extent to which regulated prices need to incorporate an option to delay, depend on the nature of demand uncertainty.