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.     

Stakeholders’ relationships and product market competition

In this article, we study the relationships between main stakeholders (shareholders, consumers and employees) when firms are consumer oriented (CO) in the sense of caring about consumers’ interests in the objective function. We let these firms first bargain with labour union over their employees’ wages and then compete either in the quantity space (Cournot competition) or in the price space (Bertrand competition). Our model shows that taking care of the consumers’ interests when determining product market strategies may reverse the traditional ranking between Cournot and Bertrand equilibria. This implies that if shareholders in a CO firm can choose either a quantity or a price strategy, they will surprisingly choose the latter. Moreover, we show that the conflicting interests between main stakeholders are attenuated under Bertrand competition compared to Cournot competition.     

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).     

Costly horizontal differentiation

We study the effect of quadratic differentiation costs in the Hotelling model of endogenous product differentiation. The equilibrium location choices are found to depend on the magnitude of the differentiation costs (relatively to the transportation costs supported by consumers). When the differentiation costs are low, there is maximum differentiation. When they are high, there is partial differentiation, with a degree of differentiation that decreases with the differentiation costs. In any case, the socially optimal degree of differentiation is always lower than the equilibrium level. We also study the case of collusion between firms. If firms can combine locations but not prices, they locate asymmetrically when differentiation costs are high and choose maximum differentiation when they are low. When collusion extends to price setting, there is partial differentiation.     

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.     

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.     

Foreign market entry,upstream market power,and endogenous mode of downstream competition

In a differentiated duopoly model of trade and FDI featuring both horizontal and vertical product differentiation, we examine whether globalization and trade policy measures can generate welfare gains by leading firms to change their mode of competition. We show that when a high-quality foreign variety is manufactured under large frictions due to upstream monopoly power, a foreign firm can become a Bertrand competitor against a Cournot local rival in equilibrium, especially when the relative product quality of the foreign variety is sufficiently high and trade costs are sufficiently low (implying higher input price distortions due to double marginalization). Our results suggest that such strategic asymmetry is welfare improving and that the availability of FDI as an alternative to trade can make welfare-enhancing strategic asymmetry even more likely, especially when both input trade costs and fixed investment costs are sufficiently low and trade costs in final goods are sufficiently large.     

Information quality choice and information disclosure in oligopoly

In this paper, we provide a framework to analyze the information disclosure and information quality choice in the oligopoly in which one firm has the opportunity to choose her information quality flexibly and then decide her information disclosure rule after she has observed her information.We find that in the Cournot (Bertrand)competition, when the goods are substitutes (complements) and the degree of substitution (complement) is small enough, the firm will choose the maximal information quality. However, if the degree of substitution (complement) is large enough, the information quality is some intermediate value. On the other hand, in the Cournot (Bertrand) competition, when the goods are complements (substitutes), the maximal information quality will be chosen. We also find that the Fully Revealing case in which the probability of information disclosure is one will occur in (i) the Cournot competition with sufficiently small degree of substitution; (ii) the Cournot competition when goods are complements; (iii) the Bertrand competition when goods are substitutes; (iv) the Bertrand competition with sufficiently small degree of complements. Moreover, we show that the No Revealing case in which the probability of information disclosure is zero will never show up.     

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.     

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 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.     

Location equilibrium with asymmetric firms: the role of licensing

It is known that if exogenous cost heterogeneities between the firms in a spatial duopoly model are large, then the model does not have a pure-strategy equilibrium in location choices. It is also known that when these heterogeneities are stochastically determined after firms choose their locations, spatial agglomeration can appear. To tackle these issues, the current paper modifies the spatial framework by allowing firms to exchange the cost-efficient production technology via royalties. It is shown that technology transfer guarantees the existence of a location equilibrium in pure strategies and that maximum differentiation appears in the market.     

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.     

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.     

Equilibrium prices in the Bertrand and Cournot oligopolies

The equilibrium prices for the Bertrand and Cournot oligopolies with product differentiation are compared. If all firms have linear demand and cost functions, and if, in addition, the Jacobian matrix of the demand functions has a dominant negative diagonal, the Cournot equilibrium prices are not lower than the Bertrand ones. The general condition for the comparison of the Bertrand and Cournot equilibrium prices can be derived even if the nonlinearity is involved in the cost and/or demand functions.     

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.     

Spatial Cournot competition in a circular city with more than two dispatches

This paper investigates spatial Cournot competition in a circular city, where the maximal service range of a vehicle is less than half of the perimeter, and a firm needs to initiate more than two dispatches to serve the whole market. We examine a multi‐stage game of location and transportation mode choices, and the subsequent quantity competition between duopoly firms. The findings reveal that non‐maximum dispersion is the unique location equilibrium when duopoly firms deliver products in different transportation modes or when the transportation mode decisions are made endogenously and the fixed cost of a transportation instrument is relatively high.     

An Observable Delay Game with Unionised Managerial Firms

The endogenous order of moves is analysed in a unionised Cournot duopoly with managerial delegation and firm‐specific unions, where firms choose whether to set quantities sequentially or simultaneously. It is shown that, in contrast to the standard duopoly with profit‐maximising firms where both firms prefer to be the leader and thus simultaneously chosen quantities emerge as an endogenous equilibrium, a rich set of equilibrium outcomes may occur. In particular, the result of sequential choices, which reverses the conventional wisdom in regard to Cournot duopolies, emerges as the endogenous equilibrium when the union's wage orientation is sufficiently high.     

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.