ON COURNOT-BERTRAND MIXED DUOPOLIES*

This paper deals;with a situation where a quality-setting Cournot firm and a price-seeting Bertrand firm coexist in the same industry. Under a set of regularity conditions on demand and coast, we compute equilibrium prices on Cournot-Bertrand "mixed"duopolies, and compare them with those of "pure" Cournot and Bertrand duopolies.     

QUALITY DIFFERENTIATION,WELFARE, AND THE MODE OF COMPETITION IN A VERTICALLY DIFFERENTIATED PRODUCT MARKET: A NOTE*

We analyse the implications of quality differences in a vertically differentiated product market for social welfare by employing an endogenous quality choice model. We find that in of Bertrand and Cournot duopolies, the degree of quality differentiation at equilibrium in an unregulated market is larger or smaller, respectively, than that of the socially second‐best optimum. This implies that a reduction in quality difference, respectively, increases or decreases social welfare in the case of Bertrand or Cournot duopolies.     

Comparing Cournot and Bertrand equilibria in an asymmetric duopoly with product R&D

We compare the Cournot and Bertrand equilibria in an asymmetric duopoly with product R&D competition. If a firm’s marginal cost is lower than that of its rival, then this firm (its rival) is referred to as the more (less) efficient firm. Under each mode of competition, there are three types of equilibria: blockaded-entry, deterred-entry, and accommodated-entry. Moreover, the presence of R&D investment makes it harder for the less efficient firm to survive. Cournot competition entails a unique equilibrium, whereas Bertrand competition may yield two equilibria. It is harder for the less efficient firm to survive under Bertrand competition than under Cournot competition. Versus Cournot competition, Bertrand competition yields higher industry output, and it shifts production from the less efficient firm to the more efficient firm. This result, together with the known size effect, explains the following three findings. First, the more efficient firm has a normal output ranking, whereas the less efficient firm may demonstrate an output reversal. Second, the more efficient firm may demonstrate a R&D reversal, whereas the less efficient firm has a normal R&D ranking (its Cournot R&D effort exceeds its Bertrand R&D effort). Third, Bertrand competition is more welfare-efficient than Cournot competition.     

Renegotiation in repeated games

In repeated games, subgame-perfect equilibria involving threats of punishment may be implausible if punishing one player hurts the other(s). If players can renegotiate after a defection, such a punishment may not be carried out. We explore a solution concept that recognizes this fact, and show that in many games the prospect of renegotiation strictly limits the cooperative outcomes that can be sustained. We characterize those outcomes in general, and in the prisoner's dilemma, Cournot and Bertrand duopolies, and an advertising game in particular.     

BERTRAND Vs. COURNOT COMPETITION WITH UPSTREAM FIRM INVESTMENT

This paper compares Bertrand and Cournot competition in a vertical structure in which the upstream firm sets the input price and makes R&D investments. We show that from the downstream firms’ point of view, Cournot competition has the advantage of a more monopolistic effect, leading to the setting of a higher price, but has the disadvantage of inducing a lower incentive for the upstream firm to invest. On the other hand, Bertrand competition has the advantage of providing a greater incentive for the upstream firm to invest but has the disadvantage of a more competitive effect, leading to the setting of a lower price. Our main findings are as follows. First, R&D investment level is greater under Bertrand competition than under Cournot competition. Second, from the standpoint of the upstream firm and industry, Bertrand competition is more efficient than Cournot competition. Third, from the standpoint of the downstream firms, Bertrand competition is more efficient than Cournot when investment is sufficiently efficient and products are sufficiently differentiated.     

OPTIMUM-WELFARE AND MAXIMUM-REVENUE TARIFFS UNDER BERTRAND DUOPOLY

This article derives the maximum‐revenue tariff and the optimum‐welfare tariff under Bertrand duopoly with differentiated products. It is shown that both tariffs are lower under Bertrand duopoly than under Cournot duopoly. Also, the optimum‐welfare tariff may exceed the maximum‐revenue tariff under both Bertrand duopoly and Cournot duopoly. This result is more likely the lower the costs of the home firm relative to the costs of the foreign firm, and the greater the degree of product substitutability. Also, it is shown that the optimum‐welfare tariff is less likely to exceed the maximum‐revenue tariff under Bertrand duopoly than under Cournot duopoly.     

Regulation through a revenue contest

This paper proposes a mechanism for the regulation of duopolies a revenue contests among the firms. Under the mechanism, the firm with the lower revenue is to pay a penalty to the firm with the higher revenue proportional to the difference between their revenues. In a homogenous good Cournot duopoly with convex cost and demand functions, the mechanism implements the optimal outcome when the firms have symmetric costs. When one firm is more efficient, the mechanism leads to increased social surplus under a large set of parameters. We also consider extensions that involve cost uncertainty, repeated games and differentiated goods.     

Endogenous timing of moves in an asymmetric price-setting duopoly

This paper adds to the growing literature on endogenous timing of decisions in duopolies. We show for a price-setting duopoly game with sufficiently asymmetric and strictly convex cost functions that the less efficient firm moves first while the more efficient moves second with a higher price than the less efficient firm.Received: October 2002, Accepted: March 2003, JEL Classification: D43, L13AttilaTasnádi : attila.tasnadi@wiwi.uni-bonn.deCorrespondence to : Department of Economics, University of Bonn, Adenauerallee 24-42, 53113 Bonn, GermanyAttilaTasnádi : I am grateful to Dan Kovenock and the anonymous referees for many comments and suggestions on an earlier version of this paper. Parts of this research were done during the authors Bolyai János Research Fellowship provided by the Hungarian Academy of Sciences (MTA).     

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     

Why are firms sometimes unwilling to reduce costs?

This paper identifies the environments in which it does not pay for a multiproduct firm to engage in small cost reductions. Specifically, it shows that a multiproduct Bertrand firm’s profits will decrease in response to a small reduction in one product’s marginal cost if and only if the output share of the cost-reducing unit is below a threshold. Because cost reductions by a single-product firm or by a multiproduct Cournot firm always increase the firm’s profits, this result is unique to multiproduct Bertrand firms.     

Strategic R&D and the innovation of products: understanding the role of time preferences and product differentiation

We evaluate the effects of innovation on competition using an optimal control approach that incorporates firms' time preferences. Using a model where firm(s) innovates by investing in research and development to create a more appealing product for heterogeneous consumers, we examine conditions that maximize social welfare. When firm(s) choose discount rate regardless of market structure, a monopoly will develop more innovative products. However, we show that duopolies may increase innovation if competition alters firms' outlook. Finally, we identify firm incentives to behave myopically, which in the context of collusion may impede industry-wide innovation.     

A Two-stage Price-setting Duopoly: Bertrand or Stackelberg

This paper investigates a two-stage price-setting duopoly with differentiated goods. First, each firm announces its price; second, it chooses its actual price; and finally the market opens. Once a firm announces a price, it is able to discount it but not raise it. The model includes Stackelberg-type and Bertrand-type equilibria as possible outcomes. Whether Bertrand or Stackelberg appears in equilibrium depends on the properties of demand functions crucially. We find three patterns of equilibrium outcomes; one case has Bertrand equilibrium only, another has Stackelberg only, and the other has both equilibria     

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.     

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.     

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.     

Mixed Competition and Patent Licensing

This paper studies the patent licensing decision of an insider patentee when two firms engage in a mixed (Cournot–Bertrand or Bertrand–Cournot) competition where one firm adopts the quantity strategy while the other uses the price strategy and vice versa. If either the fixed fee or royalty is applied, then the licensor prefers the fixed fee when the licensor takes the quantity strategy, while the licensee uses the price strategy (Cournot–Bertrand). If the two‐part tariff is applied, then the two‐part tariff is more likely to be adopted by the licensor under Cournot–Bertrand than under Bertrand–Cournot competition.     

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.     

Optimal pollution control in a mixed oligopoly with research spillovers

We study optimal pollution abatement under a mixed oligopoly when firms engage in emissions‐reducing research and development (R&D) with imperfect appropriation. The regulator uses a tax to curb emissions. Results show that in a mixed oligopoly, the public firm has positive emissions reduction in equilibrium; however, emissions reductions of the private firm could be positive or zero. Under certain conditions, the optimal pollution tax is positive; otherwise, the tax reverts to a subsidy. Comparing mixed and private duopolies, privatisation leads to reductions in R&D and output, but to an increase in overall emissions, so privatisation tends to make the environment worse.     

On Licensing Under Bertrand Competition

This paper considers licensing by an innovating firm to its competitor in a differentiated duopoly with Bertrand competition. A principal finding is that royalty licensing may be superior to fee licensing for the innovating firm both when the innovation is drastic and when the innovation is non-drastic.