Kreps & Scheinkman with Product Differentiation

Kreps and Scheinkman (1983)’s celebrated result is that in a two-stage model of a market with homogeneous products in which firms noncooperatively pick capacities in the first stage and set prices in the second stage, the equilibrium outcome is that of a one-shot Cournot game. This note derives capacity best response functions for the first stage and extends the Kreps and Scheinkman result to the case of differentiated products.     

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.     

Feasibility of predatory pricing in a capacity-constrained duopoly

Predatory pricing is feasible only if the minimax profit of the prey is strictly smaller than the expected profit in the corresponding Bertrand-Nash equilibrium. We completely characterize the conditions for feasibility of predatory pricing in Kreps and Scheinkman's model of capacity-constrained duopoly. The predator must have a capacity larger than that of the prey, and also larger than the Cournot capacity. Surprisingly, predatory pricing may be infeasible not only if the prey is too large but also if it is too small.     

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.     

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.     

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 versus quantity in a duopoly of vertical differentiation with loss-averse consumers

In a model à la Mussa and Rosen (1978) in which consumers are loss-averse, I check the robustness of the result obtained by Tanaka (2001). As he did, I find that the quantity contract is a dominant strategy for both firms. Thus, Cournot is the outcome in equilibrium. Finally, I find that loss aversion in general intensifies competition.     

Strategic interaction between futures and spot markets

We study an oligopolistic industry where firms are able to sell in a futures market at infinitely many moments prior to the spot market. A kind of Folk-theorem is established: any outcome between perfect competition and Cournot can be sustained in equilibrium. We then find that the Cournot outcome can be sustained by a renegotiation-proof equilibrium. However, this is not true for the competitive outcome. Furthermore, only the monopolistic outcome is renegotiation-proof if firms can buy and sell in the futures market. These results suggest, contrary to existing literature, that the introduction of futures markets may have an anti-competitive effect.     

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.     

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.     

The Optimal Privatization Policies under an International Mixed Duopoly

This paper explores the socially optimal privatization policies under the setting of international mixed duopoly. We find that partial privatization is socially optimal under Cournot competition and private leadership competition, whereas full nationalization is socially optimal under public leadership competition. Moreover, the equilibrium social welfare under private leadership competition is higher than that observed under Cournot competition and that observed under private leadership competition, which differs from the findings of Matsumura ( 2003b ). We also show that the endogenous timing game has a subgame perfect Nash equilibrium outcome, under which the government chooses a partial privatization policy, and private leadership competition emerges as the optimal output decision sequence of firms. An important policy implication from this paper is that the government should partially privatize the public firm and facilitate the emergence of private leadership competition in an international mixed market.     

The dynamics of a differentiated duopoly with quantity competition

We analyse the dynamics of a Cournot duopoly with heterogeneous players to investigate the effects of micro-founded differentiated products demand on stability. The present study, which indeed modifies and extends Zhang et al. (2007) (Zhang, J., Da, Q., Wang, Y., 2007. Analysis of nonlinear duopoly game with heterogeneous players. Economic Modelling 24, 138–148) and Tramontana, F., (2010) (Tramontana, F., 2010. Heterogeneous duopoly with isoelastic demand function. Economic Modelling 27, 350–357), reveals that a higher degree of product differentiation may destabilise the market equilibrium. Moreover, we show that a cascade of flip bifurcations may lead to periodic cycles and ultimately chaotic behaviours. Since a higher degree of product differentiation implies weaker competition, then a theoretical implication of our findings, that also constitute a policy warning, is that a fiercer (weaker) competition tends to stabilise (destabilise) the unique positive Cournot–Nash equilibrium.     

A note on merger in mixed duopoly: Bertrand versus Cournot

In this note we analyze the incentives to merge in a mixed duopoly if firms compete in prices or quantities. Our model framework mainly follows Barcena-Ruiz and Garzon (J Econ 80:27–42, 2003) who set up the model with quantity competition. We extend their analysis by analyzing the case of competition in prices. Further we compare the incentives to merge with Bertrand and Cournot competition. Comparing quantity with price competition we can show that a merger is more likely with Cournot competition than with Bertrand competition.     

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.     

Macroeconomic effects of an indirect tax substitution

We study an indirect tax reform in a general equilibrium model with imperfect competition for both the Cournot and the Free entry equilibria. We show that it is possible to attain a positive balanced budget multiplier by means of a substitution of specific by ad valorem taxation. Moreover, although any tax substitution causes higher prices and the flow up of firms in the long-run, the Free entry equilibrium output can increase with respect to that of the Cournot equilibrium. Finally, in contrast with the partial equilibrium, welfare decreasing tax reforms are likely to occur even when the balanced budget multiplier is positive.      

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     

Tariff Revenue Competition in a Free Trade Area: The Case of Asymmetric Large Countries

The striking result has been shown by Richardson that tariff revenue competition between two symmetric member countries of a free trade area (FTA) results in complete elimination of external tariffs if there exists a pure‐strategy Nash equilibrium at all. Richardson also conjectures without building a model that if member countries are asymmetric in market size, there exists a pure‐strategy Nash equilibrium in which both countries set positive external tariffs. We explicitly extend his tariff competition model into the case of asymmetric FTA member countries, and confirm his conjecture. We also show that there exists a mixed‐strategy Nash equilibrium in the case of symmetric countries.     

Free and second-best entry in oligopolies with network effects

We compare the number of firms in equilibrium in a Cournot industry with positive network effects and complete compatibility, under free and second-best entry. Under free entry, the firms decide whether to enter the market or not; in the second-best problem, the number of firms is established by the regulator to maximize social welfare (the regulator controls entry but not production). We show that when individual equilibrium output decreases with entry (business-stealing competition), free entry may lead to more or less firms than the second-best problem. This contrasts with the standard (nonnetwork) Cournot oligopoly model, wherein with business-stealing competition, free entry leads to an excessive number of firms compared with the second-best solution.     

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.