Costly Search, Capacity Constraints, and Bertrand Equilibrium Price Dispersion

This article analyzes the impact of transaction (search) costs and capacity constraints in an almost competitive market with homogeneous firms that compete on price. We characterize conditions under which Nash equilibria with price dispersion exist; in equilibrium, firms play pure strategies in prices and consumers adopt a symmetric mixed search strategy. Price dispersion is possible even though consumers all have the same search cost and valuation for the item and prices charged by all firms are common knowledge.     

Consumer flexibility,data quality and location choice

We analyze firms’ location choices in a Hotelling model with two-dimensional consumer heterogeneity, along addresses and transport cost parameters (flexibility). Firms can price discriminate based on perfect data on consumer addresses and (possibly) imperfect data on consumer flexibility. We show that firms’ location choices depend on how strongly consumers differ in flexibility. Precisely, when consumers are relatively homogeneous, equilibrium locations are socially optimal regardless of the quality of customer flexibility data. However, when consumers are relatively differentiated, firms make socially optimal location choices only when customer flexibility data becomes perfect. These results are driven by the optimal strategy of a firm on its turf, monopolization or market-sharing, which in turn depends on consumer heterogeneity in flexibility. Our analysis is motivated by the availability of customer data, which allows firms to practice third-degree price discrimination based on both consumer characteristics relevant in spatial competition, addresses and transport cost parameters.     

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.     

Informative advertising by heterogeneous firms

This paper introduces a model to analyze the role of the cost of information dissemination in large markets where firms have varying degrees of intrinsic efficiency reflected in their marginal costs. Firms enter a market and discover how efficient they are. Those firms with high enough efficiency stay, others exit. Remaining firms then compete to attract consumers by disseminating information about their existence and their prices using a common advertising technology. The properties of the model’s equilibrium are analyzed. The model is then used to study the effect of the cost of information dissemination on the competitiveness of the market and key industry aggregates, such as price distribution and the distribution of firm value.     

Price Competition and Consumer Externalities in a Vertically Differentiated Duopoly with Information Disparities

In this paper, we extend the model of vertical product differentiation to consider information disparities about quality differences and their effects on price competition. If uninformed consumers overestimate vertical differentiation, asymmetric information is a source of market power and informed consumers exert positive externalities on high quality product purchasers and negative externalities on low quality product purchasers. Such a result is consistent with the fact that information undermines brand. If uninformed consumers are skeptical, adverse selection issues arise and market demands may be perfectly inelastic to prices. With elastic demands equilibrium prices may be either distorted downwards or reflect real quality if the share of informed consumers is suffciently high. Therefore, with skeptical consumers firms may want either to signal quality or subsidize information provision.     

TALKING,SEARCHING, AND PRICING*

I study the implications of interpersonal communication for incentives for consumers to acquire information and firms’ pricing behavior. Firms market a homogeneous product and choose its price; consumers acquire price information at some cost to themselves. Also, each consumer accesses the information acquired by a sample of other consumers—interpersonal communication. An exogenous increase in the level of interpersonal communication decreases the information that consumers acquire, and, when search costs are low, firms price less aggressively. In an extension, consumers may choose to invest in interpersonal communication at some cost. A decrease in the costs of interpersonal communication decreases firms’ competition.     

Capacity precommitment and price competition yield the Cournot outcome

We introduce a simple model of oligopolistic competition where firms first build capacity, and then, after observing the capacity decisions, choose a reservation price at which they are willing to supply their capacities. This model describes many markets more realistically than the model of Kreps and Scheinkman [Kreps, D., Scheinkman, J., 1983. Quantity precommitment and Bertrand competition yield Cournot outcomes. Bell J. Econ. 14, 326–337]. We show that in this new model every pure strategy equilibrium yields the Cournot outcome, and that the Cournot outcome can be sustained by a pure strategy subgame perfect equilibrium.     

Price dispersion in a model of identical agents with perfect information

Abstract. The objective of this paper is to demonstrate that price dispersion is possible even in a world of perfect information and identical consumers and firms. The driving force in the model is service capacity and congestion cost. Each firm chooses a service capacity. Customers of a firm bear a congestion cost which, for a fixed service capacity, is an increasing function of the number of customers served by this firm. We demonstrate that under certain conditions the combined profit of two firms and the total surplus are higher in a price-dispersion equilibrium than in a single-price equilibrium.     

Sequential location equilibria under incomplete information

Summary We consider a simple model of incomplete information in location theory. Two firms compete in a two stage framework: a sequential location stage and a price competition stage. Firm 1 knows both its own constant marginal cost technology and that of Firm 2, whereas the latter has incomplete information about firm 1's technology. The location stage turns out to be a monotonic signaling game and theunique D1 equilibrium is a pure strategy separating equilibrium if firm 1's cost advantage is below some bound, and otherwise a pooling equilibrium if the prior probability that Firm 1 is of the low cost type is high, or a semi-pooling equilibrium if it is low. This surprising result is due to the fact that the location gap between the two types of Firm 1 is bounded because of natural economic reasons, which may prevent the separation of the two types. Hence, incomplete information matters: the equilibrium locations differ quite significantly from the full information equilibrium locations.We would like to thank an anonymous referee for very helpful comments and also the participants in seminars at GREQE (Marseille), Université de Montréal, UBC, HEC (Paris), in the Location Theory session of the World Congress of the Econometric Society (Barcelona) and in the Game Theory Conference at the University of Western Ontario for their comments. We remain, of course, solely responsible for the content of the paper. Financial support from FCAR (Québec), SSHRCC (Canada) and CNRS (France) is gratefully acknowledged.     

企业差异化战略对价格和质量竞争博弈均衡解的影响研究

消费者在购买商品时不仅考虑商品价格而且还要考虑商品质量水平的需求市场,如果存在两寡头企业提供某商品,必然会导致价格和质量的竞争博弈。本文研究表明:为了达到纳什均衡状态,两企业必须采取一定的差异化策略。而且在均衡状态下,如果市场是价格敏感市场,企业的差异化程度越高,对企业和消费者都越有利;如果市场是质量敏感市场,当敏感程度相对很低时,企业的差异化程度越高,对企业和消费者也都越有利;当敏感程度一般时企业可选择适当的差异化程度使得企业和消费者同时达到最大的均衡利润;但当敏感度非常高,企业差异化程度越高对企业的均衡利润越大,可对消费者的均衡利润却越小。     

Coalition-proof supply function equilibria in oligopoly

In an industry where firms compete via supply functions, the set of equilibrium outcomes is large. If decreasing supply functions are ruled out, this set is reduced significantly, but remains large. Specifically, the set of prices that can be sustained by supply function equilibria is the interval between the competitive price and the Cournot price. In sharp contrast, when the number of firms is above a threshold we identify (e.g., three if demand is linear), only the Cournot outcome can be sustained by a coalition-proof supply function equilibrium.     

THE EXISTENCE OF EQUILIBRIUM IN A DIFFERENTIATED DUOPOLY WITH NETWORK EXTERNALITIES*

The existence of a pure‐strategy subgame‐perfect equilibrium in qualities and prices is investigated in a duopoly model of vertical differentiation where quality improvements require a quadratic variable cost and network externalities operate. We show that there exists a parameter region where the incentive to predate at the quality stage prevents firms from reaching a pure‐strategy non‐cooperative equilibrium with prices above marginal costs. If network externalities are sufficiently large, a Bertrand equilibrium with zero profits may arise, although the amount of product differentiation is strictly positive.     

A hybrid equilibrium in segmented markets: the three-firm case

In this paper, we characterize two hybrid equilibria for the three-firm case in segmented markets in which consumers not only value the product itself but also the environment within which the consumption takes place. In equilibrium, the firm with the larger population of loyal consumers chooses the monopoly price while the remaining two firms play a mixed strategy. In the duopoly case, the unique equilibrium is in mixed strategies and no firm focuses only on its loyal consumers.     

Low prices cum selective distribution versus high prices: how best to signal quality?

We investigate the best signalling strategy for a monopoly introducing a new product with unobservable quality when second-period sales are linked to first-period ones and the firm may tailor its distribution network to exclude some consumers. When producing a high quality product rather than a low quality one is relatively costly with respect to the increase in quality, optimal signalling is by price alone. But when the cost differential is lower, it will be optimal to set a low first-period price, not to serve all would-be consumers at this price (selective distribution) and raise the price afterwards. Paradoxically, this strategy allows a larger customer base to be reached than in the case of pure price signalling.     

The capital structure and investment of regulated firms under alternative regulatory regimes

This paper explains how regulated firms choose their capital structure and examines the effects of this choice on investment and on regulated prices. It is shown that in equilibrium, firms have an optimal debt level and that given this debt level, the regulated price is set high enough to ensure that firms never become financially distressed. The analysis of the equilibrium yields testable hypotheses concerning the effects of changes in cost parameters and in the regulatory climate on the equilibrium investment level, capital structure, and regulated price. The analysis also shows that a regulatory restriction on the ability of the firm to issue securities may have an adverse effect on investment and consequently may harm consumers.     

Commitment to a strategy of uniform pricing in a two-period duopoly with switching costs

This paper studies decisions by firms of whether to attempt “behavior-based” price discrimination in markets with switching costs by using a two-period duopoly model. When both firms commit themselves to a pricing policy and consumers are “sophisticated” and have rational expectations, there is a dominant strategy equilibrium with both firms engaging in uniform pricing. Both firms are better off in the uniform pricing equilibrium, compared with the discriminatory equilibrium.      

Price and Quantity Competition in a Differentiated Duopoly With Network Compatibility Effects

We consider the efficiency of price and quantity competition in a network products market, where we observe product compatibility with network externalities (hereafter, network compatibility effects). In particular, if network compatibility effects between firms are sufficiently asymmetric, the Cournot equilibrium is more efficient than the Bertrand equilibrium in terms of larger consumer, producer and total surpluses. Then, we consider an endogenous choice of the strategic variables, price and quantity. If the degree of network compatibility effects of the rival firm is larger (smaller) than the degree of product substitutability, then choosing prices (quantities) is a dominant strategy for the firm. Thus, if the network compatibility effects of both firms are larger (smaller), the Bertrand (Cournot) equilibrium arises. Furthermore, if the network compatibility effects between the firms are sufficiently asymmetric, the firm with a larger (smaller) network compatibility effect than a certain level of product substitutability chooses quantities (prices). In this case, the Cournot–Bertrand equilibrium arises, which is less (more) efficient than the Cournot equilibrium in terms of consumer (producer) surplus.     

A Model of Outsourcing and Foreign Direct Investment

This paper presents a model in which two firms may use foreign direct investment or outsourcing in order to reduce the production cost of an intermediate input. Outsourcing requires training which is costly and creates a positive spillover. The paper shows that the equilibrium depends on the level of training costs. If they are high, only bilateral outsourcing is possible in equilibrium. If bilateral outsourcing is incomplete, it will not change prices compared to no outsourcing. If they are low, only complete outsourcing is possible. If complete outsourcing is unilateral (bilateral), the price increases (decreases) with the degree of spillovers.     

ENTRY AND QUALITY SIGNALLING WHEN ONLY SOME CONSUMERS ARE INFORMED OF THE ENTRANT'S QUALITY

This paper focuses on competition between an incumbent and an entrant when only the entrant's quality is unknown to (some) consumers. The incumbent may or may not know the entrant's quality. The model reveals a separating equilibrium where the entrant's high price signals its high quality when the proportion of informed consumers is at some intermediate value. The case in which the incumbent knows the entrant's quality generates two additional equilibria. When the proportion of informed consumers is large enough, firms choose their prices as in the complete information case. The entrant's high price in combination with the incumbent's low price signals the entrant's high quality. When the proportion of informed consumers is at some intermediate value, the incumbent's high price signals the entrant's low quality, while its low price signals the entrant's high quality. Interestingly, we find that entry may be facilitated with informational product differentiation.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996