Taxation within Cournot oligopoly

When the production of output causes pollution, we often consider taxation as a means to reduce it. This paper examines various forms of taxation to control pollution within Cournot oligopoly. It shows that two commonly used forms can actually increase pollution. In contrast, both of these forms unambiguously reduce pollution within the competitive model. The paper provides conditions, in terms of demand and technology, that make taxation effective in the Cournot oligopoly case. Another implication of the analysis is that, outside the price-taking framework, asymmetry of cost functions is particularly important and deserves careful attention when we examine the effect of taxation.     

Cournot and Bertrand Games

The author describes a series of matrix choice games illustrating monopoly, shared monopoly, Cournot, Bertrand, and Stackelberg behavior given either perfect complements or perfect substitutes. The games are created by using a spreadsheet to fill out a profit table given the choices of two players. One player selects the column, the other the row, and the table gives the profit of the row chooser. Because each player has a table, each thinks of him- or herself as the row chooser and the other as the column chooser. The games may be applied to international trade through the traditional Boeing v. Airbus story or, more currently, through foreign sales corporations. Addition of Bertrand competition allows discussion of price wars, and addition of perfect complements allows discussion of the proposed Microsoft breakup.     

Teaching Cournot Without Derivatives

The author presents a simple technique for teaching the Cournot model to first-year students. The approach involves demonstrating to the students that out of all rectangles with a common perimeter, the square has the greatest area. No use is made of derivatives. The same approach can be used to understand some other market forms.     

Leibniz und Cournot

Ohne Zusammenfassung     

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     

A cake for Cournot

A cake division mechanism is presented that is equivalent in terms of the size of the pieces of the cake n players’ receive in equilibrium to the quantities that n firms in a Cournot oligopoly supply in equilibrium. This mechanism extends to equivalence between cake division and Nash’s ‘divide the dollar’ game.     

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.     

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.     

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.     

Stackelberg versus Cournot Equilibrium

We reconsider Stackelberg's classical critique of the Cournot duopoly, in the framework of endogenous timing for two-player games. For quantity duopoly we provide different sets of minimal conditions, directly on the demand and cost functions, yielding respectively the simultaneous and the two sequential modes of play. While our findings essentially confirm the predominance of the former, they also indicate that the latter is natural under some robust but restrictive conditions. No extraneous assumptions (such as concavity, existence, or uniqueness of equilibria…) are needed, and the analysis makes crucial use of the basic results from the theory of supermodular games.Journal of Economic LiteratureClassification Numbers: B21, C72, D43, L13.     

Inferior factor in Cournot oligopoly

The condition for factor inferiority has been well known for a competitive firm facing perfect competition in both product and factor markets. Whether the factor inferiority is observable or not has been unknown for oligopoly facing perfect competition in factor market. We derive a general condition for the factor inferiority in Cournot oligopoly without product differentiation. We derive it on the basis of a novel technique for proving the existence of a unique Cournot equilibrium industry output.     

Cournot games with biconcave demand

Biconcavity is a simple condition on inverse demand that corresponds to the ordinary concept of concavity after simultaneous parameterized transformations of price and quantity. The notion is employed here in the framework of the homogeneous-good Cournot model with potentially heterogeneous firms. The analysis leads to unified conditions, respectively, for the existence of a pure-strategy equilibrium via nonincreasing best-response selections, for existence via quasiconcavity, and for the uniqueness of the equilibrium. The usefulness of the generalizations is illustrated in cases where inverse demand is either “nearly linear” or isoelastic. It is also shown that commonly made assumptions regarding large outputs are often redundant.     

Cournot competition and endogenous firm size

The paper studies the dynamics of firm size in a repeated Cournot game with unknown demand function. We model the firm as a type of artificial neural network. Each period it must learn to map environmental signals to both a demand parameter and its rival’s output choice. However, this learning game is in the background, as we focus on the endogenous adjustment of network size. We investigate the long-run evolution of firm/network size as a function of profits, rival’s size, and the type of adjustment rules used.

Secret information acquisition in Cournot markets

Summary. Two-stage game models of information acquisition in stochastic oligopolies require the assumption that firms observe the precision of information chosen by their competitors before determining quantities. This paper analyzes secret information acquisition as a one-stage game. Relative to the two-stage game firms are shown to acquire less information. Policy implications based on the two-stage game yield, therefore, too high taxes or too low subsidies for research activities. For the case of heterogeneous duopoly we briefly discuss comparative statics results. Received: August 9, 1999; revised version: May 31, 2000     

Second-best trade policies in Cournot oligopoly

In this paper we study the optimal import policy in an oligopolistic market with a given number of quantity-setting firms. In the absence of fixed costs, we show that if the policy instrument is an import quota, the optimal policy is either free trade or autarky, while if the instrument is a tariff the optimal policy is neither free trade nor autarky. In the case of fixed costs, we show that contrary to the traditional protectionist argument, a restrictive import policy might increase domestic welfare by increasing domestic consumers' surplus, instead of increasing domestic profits.     

Home bias in multimarket Cournot games

We explore the role of trade costs for the home bias in trade. In a series of Cournot duopoly experiments with a home and an export market, we compare output choices when firms face different levels of trade costs. We find that there is two-way trade in identical products and that firms hold the majority market share in their home market. The resulting home bias turns out to be, however, stronger than that predicted by theory, and it even occurs without trade costs. Tacit collusion contributes to the home bias observed in our experiment but does not offer a full explanation for the phenomenon.     

Information Advantage in Cournot Oligopoly

Consider an oligopolistic industry where firms have access to the same technology but are asymmetrically informed about the environment. Even though it is commonplace to think that in this context superior information leads to higher profits, we find that under Cournot competition this is not generally the case: It holds when firms' technology exhibits constant returns to scale, but it does not necessarily hold otherwise. Journal of Economic Literature Classification Numbers: C72, D43, L13.