Optimal punishments in linear duopoly supergames with product differentiation

We analyze optimal penal codes in both Bertrand and Cournot supergames with product differentiation. We prove that the relationship between optimal punishments and the security level (individually rational discounted profit stream) depends critically on the degree of supermodularity in the stage game, using a linear duopoly supergame with product differentiation. The security level in the punishment phase is reached only under extreme supermodularity, i.e., when products are perfect substitutes and firms are price setters. Finally, we show that Abreu's rule cannot be implemented under Cournot behavior and strong demand complementarity between products.     

Price competition in a differentiated products duopoly under network effects

We examine price competition under product-specific network effects, in a duopoly where the products are differentiated both horizontally and vertically. We emphasize the role of consumers’ expectations formation. When expectations are not influenced by prices, the market may be shared but shares must be equal unless product qualities differ or one firm, possibly even the low-quality one, may capture the entire market. When expectations are influenced by prices, which would be the case when there is commitment, competition becomes more intense and the high-quality firm tends to capture a larger market share. Under strong network effects there is a continuum of equilibria and the higher the prices, the smaller the difference between those prices can be. Requiring continuity of expectations, however, delivers a unique equilibrium where one firm captures the entire market.     

Profitability of price and quantity strategies in a duopoly with vertical product differentiation

Using a model according to Mussa and Rosen (1978) and Bonanno and Haworth (1998) we consider a sub-game perfect equilibrium of a two-stage game in a duopolistic industry in which the products of the firms are vertically differentiated. In the industry, there are a high quality firm and a low quality firm. In the first stage of the game, the firms choose their strategic variables, price or quantity. In the second stage, they determine the levels of their strategic variables. We will show that, under an assumption about distribution of consumers' preference, we obtain the result that is similar to Singh and Vives (1984)' proposition (their Proposition 3) in the case of substitutes with nonlinear demand functions. That is, in the first stage of the game, a quantity strategy dominates a price strategy for both firms. Received: April 23, 1999; revised version: May 31, 2000     

Learning in asymmetric duopoly markets: competition in information and market correlation

This paper explores experimentation and learning in asymmetric duopoly markets with product differentiation and demand uncertainty. We define the concepts of strategic substitutability and strategic complementarity in information and we show how both the mode of information competition and the transmission of information across markets affect duopoly experimentation. We relate information competition with market competition and we find that, when goods are substitutes and the correlation between market shocks is negative, firms will have a higher incentive to experiment in asymmetric markets than in symmetric ones. The opposite result follows when such correlation is positive. Also, when goods are complements the above findings are reversed.JEL Classification: D83, C72The authors thank partial financial support from the Spanish Ministry of Science and Technology under project B2000-1429, from the Spanish Ministry of Education and Science under project SEJ2004-07554 and from the “Generalitat Valénciana” under project GRUPOS04/13.     

Trade liberalization in a differentiated duopoly reconsidered

Constructing a model of differentiated Cournot duopoly, we consider welfare effects of trade liberalization (i.e. reductions in transport costs). We examine both multilateral trade (i.e. the firms in both countries export bilaterally) and unilateral trade, under which foreign entry is possible but the home firm cannot export. Some new results on trade gains under differentiated oligopoly are proved and their implications are discussed.     

Price leadership in a duopoly with capacity constraints and product differentiation

This paper analyzes Stackelberg price leadership in a duopoly in which firms are capacity constrained and products are imperfect substitutes. Assuming symmetric substitutes, linear demand, and efficient rationing, we characterize the equilibria with an exogenously specified leader. Using the equilibrium profits derived from these games, we argue that over certain ranges of asymmetric capacities an endogenous price leader will emerge. When endogenous leadership does arise, it is the large capacity firm which is the leader. We thus provide a game theoretic model of dominant firm price leadership.Dave Furth's research has been undertaken as a part of the project Competition and Cooperation. Dan Kovenock has benefited from financial support from Erasmus University Rotterdam, the Krannert School of Management, and the Jay N. Ross Young Faculty Research Fellowship. We are grateful to Tom Faith for valuable research assistance. We have benefited from the comments of the editor, two anonymous referees, and participants at the European meetings of the Econometric Society in September 1989 and the North American Winter Meetings of the Econometric Society in December 1989.     

Mixed ownership in a mixed duopoly with differentiated products

We determine optimal privatization in a symmetric differentiated duopoly when the public firms do not bear the full cost of production and hence their objective functions differ from the government’s objective function. In the social optimum firms will generally have mixed ownership, and it will depend on the type of uncovered cost, the degree of substitutability of the two products and the output decision rule of the partially public firms. Different types of mixed duopoly emerge, ranging from both firms being partially privatized, to one being fully privatized. We also derive an optimal tax-subsidy scheme as a substitute for privatization.      

Deterministic heterogeneity in tastes and product differentiation in the K-logit model

In this paper we use the K-deformed multinomial logit model to study product differentiation. The focus is on the economic interpretation of the deformation parameter which is the key parameter of this model. Then we establish the relationship between this parameter and probability choice, price elasticity and markup.     

Price discrimination and price dispersion in a duopoly

This paper analyses the problem of price discrimination in a market where consumers have heterogeneous preferences both over a horizontal parameter (brand) and a vertical one (quality). Discriminatory contracts are characterized for different market structures. It is shown that price dispersion, i.e. the observed range of prices for each class of customers, increases almost everywhere as competition is introduced in the market.     

Cartel sustainability with vertical product differentiation: Price versus quantity competition

In the context of a vertically differentiated duopoly, we analyse the influence of the degree of differentiation on cartel sustainability, under both price and quantity competition. We find that, under both Bertrand and Cournot competition, the effect of vertical product differentiation on sustainability of the collusive equilibrium is unclear. It is shown that, given a degree of differentiation, price collusion is more sustainable than quantity collusion.     

A difficulty with the address models of product differentiation

Summary. In models of product differentiation and location models it is implicitly assumed that consumers can afford to buy the differentiated goods in the market. I show that with income heterogeneity there are severe existence problems of a price equilibrium in models of horizontal product differentiation with unit demand because some consumers are income-constrained. The result generalizes to other models of product differentiation, search, and switching costs. I present an alternative specification of variable individual demand in which this kind of existence problem cannot arise. Received: October 17, 1997; revised version: February 20, 1998     

Conjectural-variation models and supergames with price competition in a differentiated product oligopoly

Conjectural-variation models (CV models) are popular in empirical research as they infer the degree of market power from real data. Theorists of industrial organization, however, disapprove of them for lack of theoretical foundation arguing that dynamic reactions are forced into a static model with the strategy space and time horizon only loosely defined. The presented model follows an idea put forward by Cabral (1995) and demonstrates that the CV model can be interpreted as the joint-profit-maximizing steady-state reduced form of a price-setting supergame in a differentiated product market under optimal punishment strategies. For the symmetric two-firm case the CV parameter is shown to cover the full range of possible outcomes — from Bertrand competition to joint unconstrained monopoly — depending on the degree of product differentiation, market growth, bankruptcy risk, and the discount rate. For the asymmetric-cost case numerical calculations are provided.     

Subsidizing cooperative and noncooperative R&D in duopoly with spillovers

Comparing the effect on private R&D investments of allowing firms to cooperate in R&D with that of providing R&D subsidies reveals that in general the latter policy is more effective than the former in promoting R&D activity. Analyzing the implementation of both policies simultaneously reveals that subsidizing cooperative and noncooperative R&D leads to the same market outcome. The preferred R&D-stimulating policy is to subsidize optimally an agreement according to which firms only share the outcomes of their independent research.     

Market share dynamics in a duopoly model with word-of-mouth communication

We analyze dynamic price competition in a homogeneous goods duopoly, where consumers exchange information via word-of-mouth communication. A fraction of consumers, who do not learn any new information, remain locked-in at their previous supplier in each period. We analyze Markov perfect equilibria in which firms use mixed pricing strategies. Market share dynamics are driven by the endogenous price dispersion. Depending on the parameters, we obtain different ‘classes’ of dynamics. When firms are impatient, there is a tendency towards equal market shares. When firms are patient, there are extended intervals of market dominance, interrupted by sudden changes in the leadership position.     

On the “merger paradox” in price competition with asymmetric product differentiation

By assuming asymmetric product differentiation, we consider the “merger paradox” in price competition (or the incentive to collude in prices). We investigate whether the emergence of the merger paradox depends on the degree of product differentiation between firms. In particular, unlike Deneckere and Davidson (1985), we demonstrate that if the degree of product differentiation between the insider and outsider is sufficiently small, then they are strategic substitutes, and thus, the merger paradox arises in price competition.     

R&D subsidies in a duopoly market with outsourcing to the rival firm

This paper investigates the effects of a public uniform R&D subsidy policy in a downstream duopoly market in which a nonintegrated firm, which faces a lower marginal cost, outsources inputs from its vertically integrated rival. The findings show that, in this market structure, such a policy has relevant effects largely differentiated between downstream competitors, as it can significantly modify the relative market shares and profitability of competing firms. Unlike the standard Cournot setting augmented with R&D, results show that the subsidy policy can have different (counterintuitive) effects on R&D investments, output, and profits of the vertically integrated producer and the vertically separated firm, which hold in both cases of exogenous and endogenous (optimal) subsidy. Our findings offer some testable implications and suggest that a subsidy policy in a market with outsourcing to a rival should also consider the different effects of this approach on competitors.     

Commitment and price competition in a dynamic differentiated-product duopoly

This paper characterizes linear Markov-perfect equilibrium in a duopolistic environment where firms engage in dynamic price competition. Firms have constant (but potentially different) marginal costs and produce differentiated products. We show that, for the case of linear demand, dynamically stable Markov-perfect equilibrium prices are strictly higher than one-shot Nash equilibrium prices, but lower than fully collusive (monopoly) prices. We provide closed-form solutions for the Markov-perfect equilibrium prices which, in principle, can be estimated given data on firm demand and costs. Our results suggest that static two-stage models of price commitment are on reasonably solid ground in that they might be viewed as a reduced form for more complicated dynamic models.     

Low-quality leadership in a vertically differentiated duopoly with Cournot competition

We model a vertically differentiated duopoly with quantity-setting firms as an extended game in which firms noncooperatively choose the timing of moves at the quality stage, to show that at the subgame, perfect equilibrium sequential play obtains, with the low-quality firm taking the leader’s role.     

Endogenous timing game in a mixed duopoly with partial foreign ownership and asymmetric increasing marginal costs

This study examines a timing game in a mixed duopoly wherein public and private firms compete by taking account of the increasing marginal cost of both firms, as well as partial foreign ownership of the private firm. This study finds that if the private firm has a strong cost advantage over the public firm, public leadership is a risk dominant equilibrium irrespective of foreign ownership ratio. This result means that the cost difference between the public and private firms matters in selecting the risk-dominant equilibrium of the timing game. Additionally, if the private firm has only a weak cost advantage over the public firm, then private leadership (public leadership) is the risk dominant equilibrium if the foreign ownership ratio is (not) small.