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.     

Regulating a duopoly by a Pretend-but-Perform Mechanism

In a linear duopoly, participants are required to declare their costs under a Pretend—but—Perform Mechanism (PPM) which enforces accordance of performance with pretended (declared) cost.Specifically, under the PPM, each firm's output in reaction to rival output is to maximize profit according to declared cost. Compared with the Cournot solution before PPM Regulation, Nash implementation of the PPM induces a Cournot solution, among the make—believe firms, giving greater industry output and efficiency along with increased consumer surplus even after compensating the duopolists for decreased profits, except in a trivial case which — educatively — thruthful declarations are confined.     

Price formation in heterogeneous oligopoly

Conclusion An equilibrium price vector has been defined and its existence and function in static price formation in cases of heterogeneous oligopoly has been established. Hitherto, authors have been misled, we think, by misinterpreting the role of reaction functions, which are central to our argument. After defining and proving the existence and uniqueness of an equilibrium price vector, it is possible to construct a generalization of the wellknown equilibrium concept of the Nash-Cournot game solution. It has previously been thought that the restriction to the Cournot solution is one of the main drawbacks to using game theoretical solutions to the problem of oligopoly. We have developed a generalization of the Nash solution in order to deal with a type of reaction hypothesis which cannot be expressed in terms of the Cournot reaction function. The new set of reaction functions here introduced demonstrate conclusively that the so-called identity on a Nash and a Cournot equilibrium is only of a formal character.We would like to thank F. Delbaen, R. A. Hirschfeld and K. Okuguchi for useful comments on an earlier draft of this paper.     

The empirical content of Cournot competition

We consider the testable implications of the Cournot model of market competition. Our approach is nonparametric in the sense that we abstain from imposing any functional specification on market demand and firm cost functions. We derive necessary and sufficient conditions for (reduced form) equilibrium market price and quantity functions to be consistent with the Cournot model. In addition, we present identification results for the corresponding inverse market demand function and the firm cost functions. Finally, we use our approach to derive testable restrictions for the models of perfect competition, collusion and conjectural variations. This identifies the conditions under which these different models are empirically distinguishable from the Cournot model. We also investigate empirical issues (measurement error and omitted variables) related to bringing our testable restrictions to data.     

Locally consistent oligopolistic equilibria are Cournot–Walras equilibria

A kth-order locally consistent equilibrium is an imperfectly competitive general equilibrium point at which firms only perceive at kth-order Taylor expansion of their true demand curves. It is shown that the set of kth-order locally consistent equilibrium strategies coincides with the set of Cournot–Walras equilibria as soon as k >1, under simple regularity conditions.     

Is a Unique Cournot Equilibrium Locally Stable?

We consider a homogeneous product oligopoly, where the Cournot equilibrium is regular and unique. We show that for a duopoly, a unique Cournot equilibrium is always locally stable. For a “n” firm asymmetric cost oligopoly a unique Cournot equilibrium is locally stable under very general conditions. The sufficient conditions for local stability of a unique Cournot equilibrium are much less restrictive than what the existing literature suggests. For a symmetric cost oligopoly the unique Cournot equilibrium is almost always locally stable, except for a perverse case. Journal of Economic Literature Classification number: L13.     

Bertrand vs. Cournot equilibrium with risk averse firms and cost uncertainty

Summary. In an oligopoly game with cost uncertainty and risk averse firms, we show that Bertrand and Cournot equilibrium have different convergence properties when the market is replicated. The Cournot equilibrium price converges to the competitive price. Under very typical and somewhat general conditions, the highest Bertrand equilibrium price converges to one higher than the competitive equilibrium. We also give examples to show how to compute the limit of the highest Bertrand equilibrium prices and illustrate the ideas of the proof. We explore conditions under which the supply curve is upward sloping, a useful condition for our results. Received: April 20, 2000; revised version: May 10, 2001     

CHANGES IN DEMAND FUNCTION IN COURNOT OLIGOPOLY

Abstract.  The effects of change in the market (inverse) demand function are systematically analysed for Cournot oligopoly without product differentiation. The general comparative-static results are stated using the original data on firms' cost functions and inverse demand function. Three special models are examined in light of our results. The stability condition is shown to be insufficient for determinate comparative statics.     

Coalition-proof supply function equilibria in oligopoly

In an industry where firms compete via supply functions, the set of equilibrium outcomes is large. If decreasing supply functions are ruled out, this set is reduced significantly, but remains large. Specifically, the set of prices that can be sustained by supply function equilibria is the interval between the competitive price and the Cournot price. In sharp contrast, when the number of firms is above a threshold we identify (e.g., three if demand is linear), only the Cournot outcome can be sustained by a coalition-proof supply function equilibrium.     

Two remarks on Cournot equilibria

We describe two simple results in the theory of Cournot equilibria. The first has to do with the effect of taxation in a Cournot industry and the second describes under what conditions a Cournot equilibrium will implicity maximize an objective function. These results are probably known, but are not well known, and they seem useful enough to be worth spelling out.     

Product differentiation, process R&D, and the nature of market competition

We investigate the relationship between process and product R&D and compare the incentives for both types of R&D under different modes of market competition (Bertrand versus Cournot). It is shown that: (i) process R&D investments increase with the degree of product differentiation and firms invest more in product R&D when they can do process R&D than when they cannot; (ii) Bertrand firms have a stronger incentive for product R&D whereas Cournot firms invest more in process R&D; and (iii) cooperation in product R&D promotes both types of R&D relative to competition whereas cooperation in both types of R&D discourages R&D relative to cooperation in just product R&D.     

On the Neutrality of Profit Taxation in a Mixed Oligopoly

This paper investigates the neutrality of profit taxation in a mixed oligopoly where one (partially) public firm competes with private firms. We find that the neutrality of a profit tax is robust under a general cost and a general demand function as long as the degree of privatization is endogenously determined. This result is also true when product heterogeneity is considered under both Cournot and Bertrand competition. By contrast, if the degree of privatization is exogenously given, the profit tax neutrality holds only in the cases where the public firm is fully privatized or fully state-owned; otherwise, the neutrality breaks down.     

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.     

A GENERAL CHARACTERIZATION OF MULTIPRODUCT COURNOT COMPETITION

The problem of oligopolistic competition between multiproduct firms is analysed using a general framework, where a given number of firms have access to the same technology, and play a Cournot game, by simultaneously choosing a quantity vector.
Conditions guaranteeing the symmetry of the Cournot equilibrium are sought. The results obtained are very general, and can be given a straightforward natural economic interpretation, essentially requiring convexity of the cost function and the ruling out of pathological demand functions.     

Is the optimum quantity of money compatible with the unique price level under laissez-faire?

The purpose of this paper is to set forth a general equilibrium model to demonstrate that even if the real social costs of producing money are positive, the optimum quantity of money is incompatible with the unique price level under laissez-faire if zero-degree homogeneity of the production-maintenance cost function in M and P is assumed.     

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.     

Contributions to Cournot oligopoly theory

This work contributes to a number of questions concerning oligopoly models. In particular, uniqueness of the Cournot equilibrium point is demonstrated under the assumption that either the unit price function is differentiable and the derivative is strictly negative or the cost functions are strictly convex. Also, under the assumption of either strictly decreasing unit price function or strictly convex cost functions, it is shown that (a) the total production level at equilibrium increases with entry of additional players, (b) that cooperation between some of the players necessarily entails profit for the others, and (c) cooperative grouping causes decrease in production levels.     

Collusion in Differentiated Duopolies with Quadratic Costs

The analysis of collusion in infinitely repeated duopoly games has generally assumed that marginal cost is constant, but this note uses quadratic costs (linear marginal costs) to compare the sustainability of collusion under Bertrand and Cournot duopoly with differentiated products. It is shown that when marginal costs are sufficiently increasing in output, then it is always easier to sustain collusion under Cournot duopoly than under Bertrand duopoly for any degree of product substitutability.     

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.     

Cournot and Stackelberg Duopolies Revisited

First, conditions are derived for a leader (or a follower) to be more advantageous than a follower (or a leader) in Stackelberg duopoly with symmetric firms and without product differentiation. Second, the equilibria in Cournot and Stackelberg duopolies are compared under a set of reasonable assumptions. If the reaction function slopes upward, the Cournot duopolists' profits turn out to be lower than those of both the Stackelberg leader and follower, and the equilibrium industry output is smaller in Stackelberg duopoly than in Cournot duopoly.
JEL Classification Numbers: D21, D43, L13.