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.     

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 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     

On the role of network externalities in strategic delegation contracts with an industry-wide union

This article analyses the role of network externalities in managerial delegation contracts for differentiated products when the marginal product costs (the wage) are set by an industry-wide union. The results show that, in both Bertrand and Cournot equilibria, each owner offers a profit-oriented incentive scheme to his or her managers by penalizing sales maximization, irrespective of the strength of the network externalities. In the presence of weak network externalities and low product differentiation, firms can obtain higher profits in the equilibrium under Cournot-type quantity competition compared with that under Bertrand-type price competition. Furthermore, the wage chosen by the union is higher in the Cournot than in the Bertrand equilibrium. In the Cournot equilibrium, the wage increases with the strength of the network externalities. However, in the Bertrand equilibrium, there exists a threshold level of the degree of product differentiation.     

Competition with Congestible Networks

We analyse competition between two network providers when the quality of each network depends negatively on the number of customers connected to that network. With respect to price competition we provide a sufficient condition for the existence of a unique pure strategy Nash equilibrium. Comparative statics show that as the congestion effect gets stronger quantities will decrease and prices increase, under both Bertrand and Cournot competition. In an example with endogenous capacities it turns out that equilibrium capacities are at first increasing and then decreasing in the strength of congestion. Furthermore, capacities are higher under Cournot competition. Welfare comparisons between Bertrand and Cournot competition are unambiguous for fixed capacities, but may turn around for endogenous capacities.     

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.     

Price and quantity competition under free entry

This paper complements that of Cellini et al. (Cellini, R., Lambertini, L., Ottaviano, G. I. P., 2004. Welfare in a differentiated oligopoly with free entry: A cautionary note. Research in Economics, 58:125–33.), which shows that Cournot competition may generate higher welfare compared to Bertrand competition in an economy with free entry. Unlike them, we provide a more general proof for this result and show that Cournot competition generates higher welfare compared to Bertrand competition when the products are sufficiently differentiated. If the products are close substitutes, welfare is higher under Bertrand competition. We show that these qualitative results hold whether or not number of varieties increases market size. We also show when the active firms earn higher profits under Bertrand competition compared to Cournot competition.     

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.     

WHOLESALE PRICES AND COURNOT‐BERTRAND COMPETITION

This note considers the competing vertical structures framework with Cournot‐Bertrand competition downstream. It shows that the equilibrium wholesale price paid by a Cournot (Bertrand)‐type retailer is above (below) marginal costs of a corresponding manufacturer. This result contrasts with the one under pure competition downstream (i.e., Cournot or Bertrand), where the wholesale price is set below (above) marginal costs in case of a Cournot (Bertrand) game at the retail level.     

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.     

考虑港口收费管制的进出口贸易竞争研究

考虑港口的收费管制因素,建立了进出口贸易竞争模型。该模型由一个出口国和两个进口国组成,且各国都拥有一个港口,位于出口国的两家公司均向两个进口国销售商品,并在各个进口国展开市场竞争（古诺竞争或伯川德竞争）,各贸易国的港口根据其是否存在价格管制确定港口收费。针对进出口公司的每种竞争模式,得到了不同的港口收费管制组合下各贸易国的港口收费、港口利润和社会福利,并将竞争均衡结果进行了比较。研究发现： （1）在进出口公司古诺竞争模式下,若三个贸易国的港口都无收费管制（有收费管制）且进出口产品的差异较大 （小）时,各贸易国的社会福利和港口利润均更高; （2）在进出口公司伯川德竞争模式下,若进出口产品的差异较大 （小）,则出口国的港口利润主要取决于港口收费 （贸易量）,而进口国恰好相反; （3）当进出口产品的差异较大 （小）时,进出口公司在古诺 （伯川德）竞争模式下各贸易国的社会福利、港口利润以及港口使用费都更高。     

Effect of credible quality investment with Bertrand and Cournot competition

We show how credible revelation and ability to commit to quality choice effect equilibrium qualities and welfare when product market is either Bertrand or Cournot competition. We show that results depend on the type of competition but not generally on the cost of quality function. We show that with Bertrand competition, the equilibrium qualities are lower with credible commitment. Competition is moderated and producer surplus is higher and consumer surplus lower. With Cournot competition, higher quality will be better but lower quality will be worse with credible commitment. Consumer surplus is always greater with credible commitment and if cost does not increase too quickly with quality, producer surplus will also increase. Thus credible commitment is a collusive device with Bertrand competition but it can improve social welfare with Cournot competition. Received: February 8, 2000; revised version: February 14, 2002 RID="*" ID="*" The idea of this paper originated in the weekly workshops of Mordecai Kurz at Stanford. I am forever in debted to Mordecai and fellow students – Luis Cabral, Peter DeMarzo, John Hillas, Michihiro Kandori, Steve Langois, Patrick McAllister, Steve Sharpe, Peter Streufert, Steve Turnbull and Gyu-Ho Wang – for their criticism and encouragement. I also benefited from comments from Yi-Heng Chen, Jin-Li Hu, Kala Krishna, Jinji Naoto, Thomas J. Prusa, and Shyh-Fang Ueng at various later stages of this work. Last but not least, I am grateful for the detailed comments of the referee.     

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.     

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.     

PROFITABLE STRATEGIC DELEGATION WITH CONJECTURAL VARIATIONS

Firms delegate strategic decisions to managers because they find it profitable to do so. In the product market, when agents make conjectures about the reaction of their rivals to marginal changes in their own strategies, the set of equilibriums can be enlarged with respect to the case of no conjectures. This paper takes a duopolistic linear market parameterization where firms selling differentiated products can delegate either price or output decisions to managers. We show that it is a dominant strategy for firms to delegate no matter whether firms are Cournot or Bertrand competitors, although the equilibrium is not necessarily efficient. Futhermore, in equilibrium Cournot competition is more profitable for firms than Bertrand competition. Finally, requiring consistency in conjectures yields the same outcome no matter what type of strategic interaction and managerial choice there is on the part of firms.     

Downstream mode of competition with upstream market power

In a two-tier oligopoly, where the downstream firms are locked in pair-wise exclusive relationships with their upstream input suppliers, the equilibrium mode of competition in the downstream market is endogenously determined as a renegotiation-proof contract signed between each downstream firm and its exclusive upstream input supplier. We find that the upstream–downstream exclusive relationships credibly sustain the Cournot (Bertrand) mode of competition in the downstream market, when the goods are substitutes (complements). In contrast to previous studies, this result holds irrespectively of the degree of product differentiation and the distribution of bargaining power between the upstream and the downstream firm, over the pair-specific input price.     

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.     

Optimal access regulation with downstream competition

We analyze the setting of access prices for a bottleneck facility where the facility owner also competes in the deregulated downstream market. We consider a continuum of market structures from Cournot to Bertrand. These market structures are fully characterized by a single parameter representing the intensity of competition. We first show how the efficient component pricing rule should be modified as the downstream competitive intensity changes. We then analyse the optimal access price where a regulator trades off production efficiency and pro-competitive effects to maximize total surplus.     

Input Prices as Signals of Costs to a Downstream Rival and Customer

We consider a dual distribution channel in which a vertically integrated manufacturer competes with a downstream rival in a retail market and also sells an input to the rival. We use a signalling model with a continuum of types to examine a situation in which the manufacturer has private information on the production cost of its retail product. We show that in a separating equilibrium under Cournot (Bertrand) retail competition, the manufacturer signals the uncompetitiveness (competitiveness) of its firm by charging a smaller input price than the optimal price under complete information.     

Quasi-Competitive Cournot Oligopoly with Product Differentiation and Symmetric Firms

Since Vives (1984 ), Cheng (1985 ) and Okuguchi (1987 ), the equilibria in Bertrand and Cournot oligopolies with product differentiation have been known to differ. Okuguchi (2005 ) has shown that Bertrand price‐adjusting oligopoly with product differentiation and symmetric firms is quasi‐competitive but not perfectly competitive in the limit state of infinite number of firms. This paper formulates and analyzes two types of Cournot output‐adjusting oligopoly with product differentiation and symmetric firms, in one of which symmetric firms producing the same goods are assumed to collude, and in the other, collusion is ruled out. The limit states are shown to be different in two oligopolies but they are both quasi‐competitive.