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.     

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.     

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.     

Biased managers with network externalities

In network industry under Cournot and Bertrand competition, we examine a model when owners of firms hire biased managers who have incorrect market demand. Contrast to previous studies, we show that (i) regardless of the strength of network externalities when consumers form the responsive and passive expectations, owners realize strategic advantage by hiring biased managers to be more aggressive under Cournot and Bertrand competition, (ii) firms prefer facing passive expectations for the weak network externalities and vice versa for the strong network exteranlities under Bertrand and Cournot competition, (iii) if the network size is sufficiently large, then the prisoner's dilemma that firms hire aggressive managers no longer exists under both competition modes. As with no delegation case, we obtain the different rankings of firms' profit depending on both network externalities and forming of expectations under Cournot and Bertrand 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.     

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.     

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.     

Competition and innovation: an experimental investigation

The paper analyzes the effects of more intense competition on firms’ investments in process innovations. More intense competition corresponds to an increase in the number of firms or a switch from Cournot to Bertrand competition. We carry out experiments for two-stage games, where R&D investment choices are followed by product market competition. An increase in the number of firms from two to four reduces investments, whereas a switch from Cournot to Bertrand increases investments, even though theory predicts a negative effect in the four-player case. The results arise both in treatments in which both stages are implemented and in treatments in which only one stage is implemented. However, the positive effect of moving from Cournot to Bertrand competition is more pronounced in the former case.     

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.     

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.     

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.     

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.     

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.     

The Political Economy of Strategic Trade Policies*

This paper applies Grossman and Helpman's (1994 ) common agency model to investigate the formation of strategic export subsidy and strategic import tariff under both Cournot competition and Bertrand competition. The results of this paper indicate that even with political pressure, the Grossman–Helpman politically‐determined export policy is identical to the rent‐shifting export policy, which is export subsidy (export tax) in Cournot (Bertrand) competition. The politically‐determined import tariff will be higher than the optimal level. This paper highlights the possibility that lobbying can restore the level of trade intervention to a more efficient one in the absence of the benevolent dictator.     

Competition,strategic delegation and delay in technology adoption

This paper examines how strategic managerial delegation affects firms' timing of adoption of a new technology under different modes of product market competition. It demonstrates that strategic delegation has differential impacts on adoption dates under Cournot and Bertrand competitions. Strategic delegation with ‘own-performance’-based incentive schemes always leads to early adoption in markets with Bertrand competition compared to that under no-delegation, but not necessarily so in markets with Cournot competition. It also shows that under strategic delegation with ‘own-performance’-based incentive schemes, adoption occurs earlier (later) in markets with Cournot competition than in markets with Bertrand competition, if the degree of product differentiation is high (low). In contrast, under strategic delegation with ‘relative-performance’-based incentive schemes, adoption dates do not differ across markets with different modes of competition. It also analyses implications of firms' choice over types of managerial incentive schemes on the speed of diffusion of new technology.     

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.     

Sabotaging cost containment

We show that sabotage may be particularly profitable for a vertically-integrated provider (VIP) when its downstream rival can devote effort to reducing its operating costs. Demand-reducing sabotage limits the return the rival anticipates from its cost management activities, and thereby inhibits those activities. The resulting higher costs for the rival increase the VIP’s profit in settings where sabotage would not be profitable if the rival could not manage its operating costs. To limit sabotage by the VIP, the rival may find it profitable to intentionally diminish its ability to reduce its production costs. The diminished ability can produce Pareto gains.     

Maximum-revenue tariffs versus free trade

Welfare with the maximum-revenue tariff is compared to free-trade welfare under Cournot duopoly with differentiated products; under Bertrand duopoly with differentiated products; and under perfect competition in the case of a large country able to affect its terms of trade. Under Cournot duopoly and Bertrand duopoly, assuming linear demands and constant marginal costs, welfare with the maximum-revenue tariff is always higher than free-trade welfare. Under perfect competition, assuming linear demand and supply, welfare with the maximum-revenue tariff will be higher than free-trade welfare if the country has sufficient market power.     

Symbiotic Production and Optimal Export Policy

This paper constructs a two‐country trade model to examine the optimal policies relating to the export of final and intermediate products under Cournot as well as Bertrand competition when firms engage in symbiotic production internationally. The paper shows that given linear demand for the final product, the optimal export policies are to tax the exports of both the final and intermediate goods under symbiotic production, regardless of whether firms engage in Cournot or Bertrand competition in the final good market, which is contrary to the conventional wisdom.     

Divisionalisation and Cournot Competition Yield Bertrand Outcomes

Bertrand and Cournot model are the main frameworks in the analysis of oligopolistic competition. The outcomes from them are however different. Using a simultaneous-move two-stage game, this article shows that, in a homogeneous product market with fairly general demand, the Bertrand outcomes can be achieved by a combination of divisionalisation and ensuing Cournot competition. This finding can be viewed as an extension to or complements of Kreps and Scheinkman (1983), who show that Cournot outcomes can be achieved by quantity precommitment and Bertrand competition.