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.     

Information transmission during the trial: The role of punitive damages and legal costs

This paper studies an incomplete information model in which a preventable accident occurred. The judge determining punitive damages observes the firm's (defendant) investment decisions, but is uninformed about the firm's experience adopting safety measures. Our model allows firms to file an appeal if the judge's verdict is incorrect, which the judge may accept or reject. We identify under which conditions a separating equilibrium exists where the firm's investment decisions signal its type to the judge, who responds with a correct verdict, thus avoiding future appeals. Our paper also finds conditions under which a pooling equilibrium exists whereby the firm's investment in precaution conceals its type from the judge, who can respond with an incorrect verdict thus giving rise to appeals. Furthermore, we show that the separating equilibrium is more likely to arise if the percentage of revenue that defendants are required to pay in punitive damages decreases, if the punitive‐to‐compensatory ratio increases, and if the legal cost of filing an appeal increases.     

COLLUSIVE EQUILIBRIUM IN COURNOT OLIGOPOLIES WITH UNKNOWN COSTS*

The article studies collusive equilibria in an infinitely repeated Cournot oligopoly with unknown costs. I look at collusive pooled Perfect Bayesian equilibria and separating equilibria either with signaling or with communication. In the separating equilibria with signaling the firms play the strictly separating Bayesian Nash equilibrium in period 1 and produce the optimal incentive compatible collusive quantity vector from period 2 onwards. In the separating equilibrium with communication the optimal incentive compatible quantity vector is produced from period 1 onwards. Among these, the optimal separating equilibrium with communication gives the highest expected discounted joint profits.     

Campaign Advertising and Voter Welfare

This paper investigates the role of campaign advertising and the opportunity of legal restrictions on it. An electoral race is modelled as a signalling game with three classes of players: many voters, two candidates, and one interest group. The group has non–verifiable insider information on the candidates' quality and, on the basis of this information, offers a contribution to each candidate in exchange for a favourable policy position. Candidates spend the contributions they receive on non–directly informative advertising. This paper shows that: (1) a separating equilibrium exists in which the group contributes to a candidate only if the insider information about that candidate is positive; (2) although voters are fully rational, a ban on campaign advertising can be welfare–improving; and (3) split contributions may arise in equilibrium (and, if they arise too often, they are detrimental to voters).     

Multi-player bargaining with endogenous capacity

We study equilibrium prices and trade volume in a market with several identical buyers and a seller who commits to an inventory and then offers goods sequentially. Prices are determined by a strategic costly bargaining process with a random sequence of proponents. A unique subgame perfect equilibrium exists, characterized by no costly delays and heterogeneous sale prices. In equilibrium constraining capacity is a bargaining tactic the seller uses to improve a weak bargaining position. With capacity constraints, sale prices approach the outcome of an auction as bargaining costs vanish. The framework provides a building block for price formation in models of equilibrium search with multilateral matching, and offers a rationale for the adoption of single-unit auctions with fixed reservation price.     

Aggregate fluctuations, financial constraints and risk sharing

Summary. Private information and costly state verification often result in credit rationing in models with smooth investment, affecting both loan size and total investment. The optimal contract is derived in a dynamic stochastic growth model with capital for two types of models: one with symmetric information and the other with asymmetric information and costly state verification. When all information is observed costlessly, the equilibrium optimal contract provides complete insurance to risk-averse savers against aggregate fluctuations. When information is asymmetric and there is costly state verification, the equilibrium optimal contract provides only partial insurance against aggregate shocks. The extent of insurance is measured by the marginal rate of transformation of consumption between borrowers and lenders which is closely linked to the user cost of capital. The deadweight monitoring costs create a wedge between a borrower's cost of capital and a lender's stochastic discount factor, with two results: (i) fluctuations in the user cost of capital provides a mechanism by which aggregate shocks can be␣propagated; (ii) the distribution of capital's share of output among borrowers, lenders, and monitoring costs varies even if capital's share is constant. Capital market frictions not only amplify aggregate fluctuations but also generate cross-sectional fluctuations that may not be observable in aggregate data. Received: November 17, 1997; revised version: April 20, 1998     

On Rothschild–Stiglitz as Competitive Pooling

Dubey and Geanakoplos (Q J Econ 117:1529–1570, 2002) have developed a theory of competitive pooling, which incorporates adverse selection and signaling into general equilibrium. By recasting the Rothschild–Stiglitz model of insurance in this framework, they find that a separating equilibrium always exists and is unique. We prove that their uniqueness result is not a consequence of the framework, but rather of their definition of refined equilibria. When other types of perturbations are used, the model allows for many pooling allocations to be supported as such: in particular, this is the case for pooling allocations that Pareto dominate the separating equilibrium.     

CONTINGENT PRICES AND MONEY*

Price posting with directed search is a widely used trading mechanism. Coles and Eeckhout showed that if sellers are allowed to post prices contingent on realized demand instead of one price, then there is real market indeterminacy. In this article, we fit this contingent price‐posting protocol into a monetary economy. We show that, as long as holding money is costly, there exists a unique equilibrium rather than a continuum. In this equilibrium sellers post a low price for when the buyer is alone, a high price for when several buyers show up, and buyers randomize between sellers and money holdings.     

An Intertemporal Currency Board

The paper shows that the traditional wisdom of raising interest rates to defend a currency enriches rather than punishes the speculators. Furthermore, using high interest rates as a currency defense tool often produces the opposite effect in times of crisis. A new approach is proposed of using Hong Kong dollar "put" options as an explicit commitment by the government. The put option itself acts like an intertemporal currency board in keeping the linked exchange rate over time. This costly signaling produces a separating equilibrium that distinguishes the strength of the Hong Kong dollar from the other Asian currencies that were under pressure in 1997.     

A GOOD ADVISOR

Effective education requires strategic consideration. If students doubt the motives of teachers and advisors, then students rationally ignore the advice they receive. Valuable information is lost in such bad communication outcomes and, consequently, the quality of education suffers. In this paper, we argue that an advisor's sacrifice is an essential virtue of a good advisor for efficient communication between an advisor and a student. We model the relation between them as a signaling game. We find a separating equilibrium in which a good advisor (whose objective function truly coincides with the student's own objective function) makes a costly sacrifice that causes the student to believe what the advisor says, while a non‐good advisor (whose objective does not coincide with the student's) chooses not to make the costly sacrifice and, consequently, the student completely ignores the advisor. In fact, it turns out to be the unique equilibrium that survives the Intuitive Criterion. The model demonstrates the importance of making students aware of those aspects of the advisor's objectives that students may not realize are closely aligned with their own (e.g., the extent to which an advisor cares about students' academic and professional trajectories as evaluated by students themselves).     

Credit contracting and bidding under wealth constraints

Summary. We model credit contracting and bidding in a first-price sealed-bid auction when bidder valuation and wealth are private information. An efficient separating equilibrium exists only if the wealth levels of both bidder types are sufficiently different. If not, high-valuation bidders signal by borrowing more and using less of their wealth – this is inefficient as wealth is a cheaper source of funds. An increase in the amount of borrowing required to signal does not necessarily decrease seller expected revenue. In contrast to separating equilibria, high-valuation bidders adopt pure strategy bids in pooling equilibria. Conditions are identified under which the lower bound on winning bids is higher in pooling than separating equilibria. Received: January 22, 2001; revised version: August 28, 2001     

A signaling model of environmental overcompliance

We present a theory of unilateral regulatory overcompliance as a signaling device. Firms that have a competitive advantage in the use of a cleaner but more costly technology overcomply in order to signal to an imperfectly informed, benevolent government that compliance costs are low, thereby triggering tougher regulation. We identify the conditions under which such an overcompliance signaling equilibrium arises, showing that there may be over-overcompliance in that firms may overcomply even when tougher regulation is not socially desirable. We also discuss the differential implications of the signaling theory as compared to other theories of unilateral regulatory overcompliance.     

Bargaining over loan contracts with signaling

This paper combines a sequential bargaining game between an enterprise and a fixed number of banks with a signaling game through which the enterprise reveals her project quality as well as her market-speed on the lending market. We characterize subgame-perfect Nash equilibrium loan contracts that are supported by separating perfect Bayesian equilibria in the signaling game. In contrast to existing models of lending markets, low-quality investment projects might be rewarded with more favorable equilibrium loan contracts than high-quality projects. Also in contrast to existing models, an increase in the competitive pressure between banks reduces the aggregate welfare in our model. The reason is that more favorable loan conditions come with a greater incentive for the ‘strong’ entrepreneur to distinguish herself from her ‘weak’ counterpart through socially wasteful signaling costs.     

Signaling bargaining power: Strategic delay versus restricted offers

Summary. I study the first-round separating equilibrium of a buyer-seller bargaining game, extended to allow for asymmetric information, strategically delayed offers and offers restricted to a portion of the good. When bargaining is over a consumption good, in equilibrium the “strong” buyer uses a restricted offer if his optimal consumption path is conservative relative to the “weak” buyer. A pure restricted offer may even be a costless, efficient signal. When the good is durable, a pure strategic delay is involved in signaling a strong bargaining position if the discount factor is high. Received: June 24, 1998; revised version: May 30, 1999     

Optimal voting schemes with costly information acquisition

A group of individuals with identical preferences must make a decision under uncertainty about which decision is best. Before the decision is made, each agent can privately acquire a costly and imperfect signal. We discuss how to design a mechanism for eliciting and aggregating the collected information so as to maximize ex-ante social welfare.We first show that, of all mechanisms, a sequential one is optimal and works as follows. At random, one agent at a time is selected to acquire information and report the resulting signal. Agents are informed of neither their position in the sequence nor of other reports. Acquiring information when called upon and reporting truthfully is an equilibrium.We next characterize the ex-ante optimal scheme among all ex-post efficient mechanisms. In this mechanism, a decision is made when the precision of the posterior exceeds a cut-off that decreases with each additional report. The restriction to ex-post efficiency is shown to be without loss when the available signals are sufficiently imprecise. On the other hand, ex-post efficient mechanisms are shown to be suboptimal when the cost of information acquisition is sufficiently small.     

Signaling in a Rent‐Seeking Contest with One‐Sided Asymmetric Information

We consider a two‐player rent‐seeking Tullock contest where one player has private information about his valuation of the prize, which can be high or low. This player can send a costly signal to his opponent, i.e., he can commit to reduce the prize either by some absolute amount of money or proportionally, conditional on winning it. We show that both kinds of signaling imply completely opposite results for separating equilibria, both in terms of conditions for existence and the type of player who sends the costly signal.     

Robust equilibria under non-common priors

This paper considers the robustness of equilibria to a small amount of incomplete information, where players are allowed to have heterogeneous priors. An equilibrium of a complete information game is robust to incomplete information under non-common priors if for every incomplete information game where each player's prior assigns high probability on the event that the players know at arbitrarily high order that the payoffs are given by the complete information game, there exists a Bayesian Nash equilibrium that generates behavior close to the equilibrium in consideration. It is shown that for generic games, an equilibrium is robust under non-common priors if and only if it is the unique rationalizable action profile. Set-valued concepts are also introduced, and for generic games, a smallest robust set is shown to exist and coincide with the set of a posteriori equilibria.     

Equilibrium audit strategies against tax treaty shopping

This paper examines game‐theoretic models of tax treaty shopping. An investor can choose a direct or indirect investment route across countries to minimize tax. A tax agency can audit the investor. The audit is costly but it can give additional revenue to the tax agency. In simultaneous‐move games, regardless of whether incomplete information exists and whether a home country allows foreign tax credits, there are mixed‐strategy equilibria where the investor may choose tax‐minimizing indirect routes and the tax agency may audit the investor. This equilibrium random audit strategy helps the tax agency raise revenue and reduce treaty shopping. Comparative statics yields an implication consistent with empirical evidence. However, if the home country has a foreign tax credit system with a high tax rate, or if the tax agency observes the investor's action in a sequential‐move game, the investor always chooses the direct route, and no treaty shopping occurs in equilibrium.     

Individual and Aggregate Real Balances in a Random-Matching Model

This article investigates the characteristics of stationary single-price equilibrium in a monetary random-matching model where agents can hold an arbitrary amount of divisible money and where production is costly. At such an equilibrium, agents' money holdings are endogenously determined and uniformly bounded. A refinement of weakly undominated strategies is argued to be necessary. It is shown that a continuum of single-price equilibria indexed by the aggregate real-money balance exists if one such equilibrium exists. Equilibria with different money-holdings upper bounds, hence different distributions, but with identical aggregate real-money balances can coexist.     

Pricing and signaling with frictions

We study a market where each seller chooses the quality and price of goods and the number of selling sites. Observing sellers? choices of prices and sites, but not quality, buyers choose which site to visit. A seller?s choices of prices can direct buyers? search and signal quality. A unique equilibrium exists and is separating. When the quality differential is large, the equilibrium implements the efficient allocation with public information. Otherwise, the quality of goods and/or the number of sites created is inefficient, due to a conflict between the search-directing and signaling roles of prices.