OPTIMAL POLICY FOR PRODUCT R&D WITH ENDOGENOUS QUALITY ORDERING: ASYMMETRIC DUOPOLY*

We examine the optimal R&D subsidy/tax policy under a vertically differentiated duopoly. In a significant departure from the existing work, we consider the case of asymmetric costs of product R&D where there is a small technology gap between firms. In our analysis, the endogeneity of quality ordering is explicitly taken into account. We demonstrate the possible anti‐leapfrogging effect of R&D subsidy/tax policy. By committing to a firm‐specific subsidy schedule contingent on firms’ quality choices, the government can not only correct distortions in product quality but also select the socially preferred equilibrium. The latter role is fulfilled by preventing the technologically inferior firm from becoming a quality leader in the industry. Both Bertrand and Cournot cases are analysed.     

On the comparison of price and quantity competition under endogenous timing

This paper compares Bertrand and Cournot equilibria in a differentiated duopoly with linear demand, and asymmetric constant marginal cost under endogenous timing. It shows that endogenous timing leads to two sequential play with both leader–follower configurations in Bertrand, but simultaneous play in Cournot. Moreover, every firm’s mark-up/output ratio and the two firms’ weighted ‘average’ price are all lower, but the two firms’ weighted ‘average’ output is higher in either of the two sequential Bertrand equilibria than in the simultaneous-move Cournot equilibrium.     

Strategic Cost Reduction and Cost Revelation

Strategic cost reduction requires cost transparency. When unilateral cost revelation is feasible, strategic cost reduction indeed arises as equilibrium. If it is not feasible, however, credible revelation has to be organized, possibly by a trade association. Then, firms face a prisoners' dilemma: in Cournot duopoly, cost revelation arises as an equilibrium, but hurts firms; in Bertrand duopoly, cost concealing is the equilibrium, while firms would be better off with cost revelation. Since cost revelation is socially desirable (undesirable) in Cournot (Bertrand) competition, it should be encouraged (discouraged).     

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     

Bertrand equilibrium with subadditive costs

We show here, in contrast to recent results, that if firms have different cost functions (that are strictly subadditive), such that the ‘monopoly breakeven prices’ are different, then in a homogeneous product duopoly there is always a Bertrand equilibrium (either in pure strategies or in mixed strategies).     

PRICE AND QUANTITY COMPETITION IN A UNIONISED MIXED DUOPOLY: THE CASES OF SUBSTITUTES AND COMPLEMENTS*

We investigate a differentiated mixed duopoly in which private and public firms can choose to strategically set prices or quantities when unions are present. For the case of a unionised mixed duopoly, there exists a dominant strategy only for the public firm that chooses Bertrand competition irrespective of whether the goods are substitutes or complements; there is no dominant strategy for a private firm. Thus, we show that regardless of the nature of goods, social welfare under Bertrand competition is always determined in equilibrium, wherein Bertrand competition entails higher social welfare than Cournot competition. Moreover, our main results hold irrespective of the nature of goods, with the exception that when a sufficiently large parameter of complements is employed, the ranking of a private firm's profit is not reversed, which is in contrast to the standard findings.     

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.     

The Cournot-Bertrand profit differential: A reversal result in a differentiated duopoly with wage bargaining

This paper compares Cournot and Bertrand equilibria in a downstream differentiated duopoly in which the input price (wage) paid by each downstream firm is the outcome of a strategic bargain with its upstream supplier (labor union). We show that the standard result that Cournot equilibrium profits exceed those under Bertrand competition - when the differentiated duopoly game is played in imperfect substitutes - is reversible. Whether equilibrium profits are higher under Cournot or Bertrand competition is shown to depend upon the nature of the upstream agents’ preferences and on the distribution of bargaining power over the input price. We find that the standard result holds unless unions are both powerful and place considerable weight on the wage argument in their utility function.     

Licensing under vertical product differentiation: Price vs. quantity competition

This paper develops a duopoly model of vertical product differentiation where two domestic firms incur variable costs of quality development. These domestic firms can purchase a superior foreign technology through licensing. Outcomes between Bertrand and Cournot competition are compared. We find that licensing raises domestic welfare, and domestic welfare is higher in Bertrand than in Cournot competition regardless of whether or not domestic firms engage in licensing. Non-exclusive licensing is also found to benefit the domestic country more than exclusive licensing.     

Vertical differentiation in a Cournot industry: The Porter hypothesis and beyond

We modify the vertically differentiated duopoly model by André et al. (2009) replacing Bertrand with Cournot behaviour, and we characterise the region wherein a Porter-type result takes place. We show that the Porter hypothesis applies in an equilibrium taking always the form of a prisoner's dilemma. Moreover, whenever the asymmetry in the cost parameters between green and brown technology is not too high, a class of equilibria emerges wherein firms converge spontaneously onto the green standard as a result of dominant strategies, any environmental regulation being altogether absent.     

Unionized Bertrand Duopoly and Strategic Export Policy

The paper reports that an export subsidy is optimal for a unionized Bertrand duopoly. Following results published by Brander and Spencer ( Journal of International Economics , 1988, pp. 217–34), this establishes the robustness of export subsidization to the mode of competition (Cournot or Bertrand), and contrasts with nonunion results in the literature. If both firms are unionized and both governments pursue active trade policies, a subsidy remains optimal except for a narrow range of extreme substitutability between products. Nations with a lower opportunity cost of labor employ more aggressive policies in equilibrium.     

Dynamic efficiency of Cournot and Bertrand competition: input versus output spillovers

We consider the efficiency of Cournot and Bertrand equilibria in a duopoly with substitutable goods where firms invest in process R&D that generates input spillovers. Under Cournot competition firms always invest more in R&D than under Bertrand competition. More importantly, Cournot competition yields lower prices than Bertrand competition when the R&D production process is efficient, when spillovers are substantial, and when goods are not too differentiated. The range of cases for which total surplus under Cournot competition exceeds that under Bertrand competition is even larger as competition over quantities always yields the largest producers’ surplus.     

ENDOGENOUS TIMING AND STRATEGIC CHOICE: THE COURNOT‐BERTRAND MODEL

Cournot establishes a Nash equilibrium to a duopoly game under output competition; Bertrand finds a different Nash equilibrium under price competition. Both treat the strategic choice variable (output versus price) and the timing of play as exogenous. We investigate Cournot‐Bertrand models where one firm competes in output and the other competes in price in both static and dynamic settings. We also develop a general model where both the timing of play and the strategic choice variables are endogenous. Consistent with the conduct of Honda and Scion, we show that Cournot‐Bertrand behaviour can be a Nash equilibrium outcome.     

Bertrand vs. Cournot equilibrium with risk averse firms and cost uncertainty

Summary. In an oligopoly game with cost uncertainty and risk averse firms, we show that Bertrand and Cournot equilibrium have different convergence properties when the market is replicated. The Cournot equilibrium price converges to the competitive price. Under very typical and somewhat general conditions, the highest Bertrand equilibrium price converges to one higher than the competitive equilibrium. We also give examples to show how to compute the limit of the highest Bertrand equilibrium prices and illustrate the ideas of the proof. We explore conditions under which the supply curve is upward sloping, a useful condition for our results. Received: April 20, 2000; revised version: May 10, 2001     

Technology adoption in a differentiated duopoly: Cournot versus Bertrand

This paper shows that the cost as well as the effectiveness of technology has a differential impact on technology adoption under two alternative modes of competition. If the cost of the technology is high, Bertrand competition provides a stronger incentive to adopt technology than Cournot competition unless the effectiveness of the technology is very low. On the contrary, if the cost of the technology is low, Cournot competition fares better than Bertrand competition in terms of technology adoption by firms. This demonstrates that the commonly subscribed assumption of ‘positive primary outputs’ restricts (inflates) the scope of higher degree of technology adoption under Bertrand (Cournot) competition. Moreover, in contrast to standard welfare ranking, it shows that Cournot competition leads to higher social welfare than Bertrand competition under certain situations.     

A note on renegotiation in repeated Bertrand duopolies

Weak Renegotiation-Proofness (WRP) singles out marginal cost pricing as a unique pure-strategy equilibrium of the infinitely repeated Bertrand duopoly. We show that, with a discrete strategy space, WRP does not eliminate any relevant subgame perfect equilibrium outcome.     

Quantity competition vs. price competition under optimal subsidy in a mixed oligopoly

This paper reconsiders the literature on the irrelevance of privatization in mixed markets within which both quantity and price competition are investigated under product differentiation. By allowing for partially privatization of a state-controlled firm, we explore competition under different timings of firms' moves and derive the conditions under which an optimal subsidy allows to achieve maximum efficiency. We show that, irrespective of the mode of competition, while the ownership of the controlled firm is irrelevant when firms play simultaneously, it matters when firms compete sequentially, requiring the leader to be publicly-owned for an optimal subsidy to restore the first-best. The paper also focuses on the extent to which a subsidy is needed to attain the social optimum in the considered scenarios, providing an ordering which highlights the subsidy equivalence between Cournot (Bertrand) private leadership and simultaneous Bertrand (Cournot) under duopoly, and the dominance of the former in oligopoly.     

Innovation,licensing, and price vs. quantity competition

In this paper, we develop a differentiated duopoly model with endogenous cost-reducing R&D and review the argument on welfare effect of price and quantity competition in the presence of technology licensing. We show that, with licensing, the standard conclusion on duopoly (Singh and Vives, 1984) is completely reversed. Cournot competition induces lower R&D investment than Bertrand competition does. Moreover, Cournot competition leads to lower prices, lower industry profit, higher consumer surplus and higher social welfare than Bertrand competition.     

Moral hazard,Bertrand competition and natural monopoly

In the traditional model of Bertrand price competition among symmetric firms, there is no restriction on the number of firms that are active in equilibrium. A symmetric equilibrium exists with the different firms sharing the market. I show that this does not hold if we preserve the symmetry between firms but introduce moral hazard with a customer-sensitive probability of exposure; competition necessarily results in a natural monopoly with only one active firm. Sequential price announcements and early adoption are some equilibrium selection mechanisms that help to pin down the identity of the natural monopolist. The insights of the basic model are robust to many extensions.     

Nature of Competition and New Technology Adoption

The incentives to adopt cost‐reducing technology by firms in a horizontally‐differentiated duopoly are analysed in the present paper. Cost reduction depends on the ‘quality’ of the ‘new technology’. A firm has to procure such technology in a ‘scoring auction’. When the quality offered by the suppliers of this technology lies in the interior of the feasible range, both firms adopt the new technology regardless of the nature of competition (Cournot or Bertrand). However, when there is a corner solution, there are equilibria where only one firm (or no firm) adopts the new technology. With a corner solution the nature of competition affects the equilibrium outcomes.