Cournot Oligopoly Model Research Articles

On the Interplay between Resource Extraction and Polluting Emissions in Oligopoly

This paper offers an overview of the literature discussing oligopoly games in which polluti ng emissions are generated by the supply of goods requiring a natural resource as an input. An analytical summary of the main features of the interplay between pollution and resource extraction is then given using a differential game based on the Cournot oligopoly model, in which (i) the bearings on resource preservation of Pigouvian tax rate tailored on emissions are singled out and (ii) the issue of the optimal number of firms in the commons is also addressed.

Entry, Profit and Welfare under Asymmetric R&D Costs

We show the effects of entry of a new firm on the profits and welfare when the firms share the same initial cost of production but differ in terms of the costs of undertaking R&D. Considering a Cournot oligopoly model with innovation and linear demand and production costs, we show that entry reduces the profits of the incumbent firms and it can be welfare reducing.

Eductive learning and the rationalizability of oligopoly games

This paper extends the eductive learning approach in settings with non-atomistic agents. It shows the connection between the characterization of rationalizable sets by Basu (1991) and the seminal result by Guesnerie (1992) in the context of Cournot oligopoly models.

The stability of a Cournot oligopoly: the effects of adaptive expectations

It is crucial to characterize the long-term behaviour for oligopolistic firms by the analysis of asymptotic stability of the equilibrium. Convergent trajectories are usually preferred in the traditional market since unstable orbits may make the behaviour unpredictable. Under some fairly general and reasonable assumptions in an oligopolistic industry, a Cournot oligopoly model is constructed where each firm maximizes its profit in consideration of adaptive expectations with respect to its rivals' choices. We finally arrive at the conclusion that the introduction of adaptive expectations can contribute largely to the convergence to Nash equilibrium, making the long-run market behaviour more predictable.

Stability of the Cournot equilibrium for a Cournot oligopoly model with n competitors

In this paper a Cournot-like model is constructed with an iso-elastic demand function for n competitors. The Cournot equilibrium is constructed for general constant unit costs. Finally, it is proved that for identical unit costs the Cournot point is a sink for two or three competitors and a saddle for more than four players.

Routes to Complexity Induced by Constraints in Cournot Oligopoly Games with Linear Reaction Functions

Within a classical discrete-time Cournot oligopoly model with linear demand and quadratic cost functions, minimum and maximum production constraints are imposed in order to explore their effects on the dynamic of the system. Due to the presence of such constraints, the dynamic model assumes the form of a continuous piecewise linear map of the plane. The study of Nash equilibria of the oligopoly game, together with an analytical and numerical investigation of the different kinds of attractors of the dynamical system, shows how the presence of production constraints generates so called border collision bifurcations, a kind of global bifurcations recently introduced in the literature on non-smooth dynamical systems, which gives rise to a quite rich spectrum of dynamic scenarios, characterized by drastic changes in the qualitative dynamic properties of the system.

Tax evasion and competition

AbstractUsing a Cournot oligopoly model with an endogenous number of firms and evasion of indirect taxes, we show that more intense competition may have the negative side effect of increasing tax evasion, thereby, lowering public revenues and welfare. This will be the case if market entry costs decrease. A similar result will hold if marginal production costs fall and demand is either weakly concave, or convex and inelastic. The result of more competition, less evasion and higher public revenues will be obtained if (a) marginal production costs fall and demand is convex and elastic or (b) the demand elasticity increases. As a policy implication, we prove that tax enforcement should be intensified if there is a negative trade‐off between competition and evasion.

Domestic entry, optimum-welfare and maximum-revenue tariffs

In this paper, we examine the ranking of the maximum-revenue tariff and the optimum-welfare tariff under a linear Cournot oligopoly model without and with free entry of domestic firms. We demonstrate that in a regulated entry oligopoly with asymmetric costs, when the marginal cost of the domestic firms exceeds a critical value, the maximum-revenue tariff is higher than the optimum-welfare tariff. We then show that under free entry of domestic firms with asymmetric costs, when the fixed cost gets larger and the domestic firms become fewer, the difference between the optimum-welfare tariff and the maximum-revenue tariff becomes larger.

Solving discrete systems of nonlinear equations

We study the existence problem of a zero point of a function defined on a finite set of elements of the integer lattice Z n of the n-dimensional Euclidean space R n . It is assumed that the set is integrally convex, which implies that the convex hull of the set can be subdivided in simplices such that every vertex is an element of Z n and each simplex of the triangulation lies in an n-dimensional cube of size one. With respect to this triangulation we assume that the function satisfies some property that replaces continuity. Under this property and some boundary condition the function has a zero point. To prove this we use a simplicial algorithm that terminates with a zero point within a finite number of iterations. The standard technique of applying a fixed point theorem to a piecewise linear approximation cannot be applied, because the ‘continuity property’ is too weak to assure that a zero point of the piecewise linear approximation induces a zero point of the function itself. We apply the main existence result to prove the existence of a pure Cournot–Nash equilibrium in a Cournot oligopoly model. We further obtain a discrete analogue of the well-known Borsuk–Ulam theorem and a theorem for the existence of a solution for the discrete nonlinear complementarity problem.

An indistinguishability result on rationalizability under general preferences

In this paper, we show that, in the class of games where each player’s strategy space is compact Hausdorff and each player’s payoff function is continuous and “concave-like,” rationalizability in a variety of general preference models yields the unique set of outcomes of iterated strict dominance. The result implies that rationalizable strategic behavior in these preference models is observationally indistinguishable from that in the subjective expected utility model, in this class of games. Our indistinguishability result can be applied not only to mixed extensions of finite games, but also to other important applications in economics, for example, the Cournot–oligopoly model.

Two-Aggregate Games: A Method of Analysis and an Example

The analysis of several economic problems such as public-good provision, contest theory and Cournot oligopoly models has benefited from exploiting the observation that a single aggregate provides a sufficient statistic for the implied non-cooperative game with many heterogeneous players. This idea is extended to analyze games in which an allocation is described by two aggregates. We suggest a method for analyzing such models, and illustrate it at work on a model of production and appropriation. We then indicate other potential applications of our method.

A Unionized Oligoply with Bounded Rational Agents

In this model I show why unions sometimes do not reduce wages, even if it will be profitable for themselves and the economy. The reasons are simple. When I allow unions and firms to be bounded rational agents with limited information, it is individually rational for unions to behave like this. Quantities firms produce approximate the collusive quantity with exogenous cost which would be an equilibrium result in a Cournot-Oligopoly Industrial Organization model. In addition this is a stable result and it is established even if firms only have sparse information about the environment and their decision rule is very simple. Hence, firms are the winners in our setting, compared to IO models. This is true on the condition that firms change quantities more often than wage bargaining takes place.

Customs Unions among Producing Countries with Different Costs

The effects of production cost asymmetries on the sustainability of customs unions among producing countries are investigated using a homogeneous-product Cournot oligopoly model, in which three producing countries subsidize exports of an homogeneous good to a consumer country that imposes a tariff on imports. It is found that the only sustainable customs union is the one formed by the three-member customs union. However, although the said customs union will be in equilibrium if utility transferences among member countries are allowed, it could not be in equilibrium if such transferences are not allowed.

A Free Lunch in the Commons

We derive conditions under which cost-increasing measures - consistent with either regulatory constraints or fully expropriated taxes - can increase the profits of all agents active within a common-pool resource. This somewhat counterintuitive result is possible regardless of whether price is exogenously fixed or endogenously determined. Consumers are made no worse off and, in the case of an endogenous price, can be made strictly better off. The results simply require that total revenue be decreasing and convex in aggregate effort, which is an entirely reasonable condition, as we demonstrate in the context of a renewable natural resource. We also show that our results are robust to heterogeneity of agents and, under certain conditions, to costless entry and exit. Finally, we generalize the analysis to show its relation to earlier work on the effects of raising costs in a model of Cournot oligopoly.

Firm Heterogeneity and Wages in Unionised Labour Markets: Theory and Evidence

In many countries wages are set in two stages, where industry-level collective bargaining is followed by firm-specific arrangements determining actual paid wages as a mark-up on the industry wage floor. What explains the wage set in each of these stages? In this paper we show that both the industry wage floor and the average wage cushion are systematically associated with the degree of firm heterogeneity in the industry: The former (latter) is negatively (positively) associated with the productivity spread. Furthermore, since the response of the wage floor dominates that of the wage cushion, workers in more heterogeneous industries tend to get lower actual paid wages. These conclusions are reached in a model of Cournot oligopoly with firm productivity heterogeneity and a two-tiered wage setting system. They are then confirmed by administrative data covering virtually all workers, firms and collective bargaining agreements of the Portuguese private sector for the period 1991-2000.

Imitators and Optimizers in Cournot Oligopoly

We present a formal model of symmetric n-firm Cournot oligopoly with a heterogeneous population of optimizers and imitators. Imitators mimic the output decision of the most successful firms of the previous round a la Vega-Redondo (1997). Optimizers play a myopic best response to the opponents' previous output. The dynamics of the decision rules induce a Markov chain. As expression of bounded rationality, firms are allowed to make mistakes and deviate from the decision rules with a small probability. Applying stochastic stability analysis, we find that the long run distribution converges to a recurrent set of states in which imitators are better off than are optimizers. This finding appears to be robust even when optimizers are more sophisticated. It suggests that imitators drive optimizers out of the market contradicting a fundamental conjecture by Friedman (1953).

Optimal tariffs of preferential trade agreements and the tariff complementarity effect

PurposeThe purpose of this paper is to evaluate and contrast the welfare effects of free trade agreements (FTAs) and customs unions (CUs) on member and non‐member countries when tariffs of both members and non‐members are endogenously determined. It also aims to provide sufficient conditions under which both types of preferential trade agreement (PTA) are likely to lower tariffs on non‐members relative to that under most favored nation (MFN).Design/methodology/approachThe paper employs a three country Cournot oligopoly model of trade with segmented markets.FindingsIt is shown that under symmetry CU members enjoy higher welfare relative to that under an FTA or MFN. Furthermore, the non‐member country gains from the formation of a PTA so long as the PTA's external tariff falls below a certain threshold. However, for FTA members to necessarily gain, their external tariff needs to be greater than this threshold but smaller than twice their MFN tariffs. Outside this tariff range, welfare effects of FTAs are ambiguous in the absence of further assumptions. The paper also isolates sufficient conditions under which a PTA member is less likely to impose a positive tariff on the non‐member relative to that under MFN.Originality/valueUnlike existing literature, we do no assume demand linearity to obtain our main welfare results and use this assumption only for illustrative purposes. Another contribution of the paper is to provide sufficient conditions under which a PTA member is less likely to impose a positive tariff on the non‐member relative to that under MFN.

Firm heterogeneity and wages in unionised labour markets: Theory and evidence

In many countries wages are set in two stages, where industry-level collective bargaining is followed by firm-specific arrangements determining actual paid wages as a mark-up on the industry wage floor. What explains the wage set in each of these stages? In this paper we show that both the industry wage floor and the average wage cushion are systematically associated with the degree of firm heterogeneity in the industry: The former (latter) is negatively (positively) associated with the productivity spread. Furthermore, since the response of the wage floor dominates that of the wage cushion, workers in more heterogeneous industries tend to get lower actual paid wages. These conclusions are reached in a model of Cournot oligopoly with firm productivity heterogeneity and a two-tiered wage setting system. They are then confirmed by administrative data covering virtually all workers, firms and collective bargaining agreements of the Portuguese private sector for the period 1991–2000.

Solving Discrete Systems of Nonlinear Equations

We study the existence problem of a zero point of a function defined on a finite set of elements of the integer lattice of the n-dimensional Euclidean space. It is assumed that the set is integrally convex, which implies that the convex hull of the set can be subdivided in simplices such that every vertex is an element of the integer lattice and each simplex of the triangulation lies in a cube of size one. With respect to this triangulation we assume that the function satisfies some property that replaces continuity. Under this property and some boundary condition the function has a zero point. To prove this we use a simplicial algorithm that terminates with a zero point within a finite number of iterations. The standard technique of applying a fixed point theorem to a piecewise linear approximation cannot be applied, because the `continuity property' is too weak to assure that a zero point of the piecewise linear approximation induces a zero point of the function itself. We apply the main existence result to prove the existence of a pure Cournot-Nash equilibrium in a Cournot oligopoly model. We further obtain a discrete analogue of the well-known Borsuk-Ulam theorem and a theorem for the existence of a solution for the discrete nonlinear complementarity problem.

Cournot equilibrium: modern techniques applied to an old problem

The Cournot oligopoly model was introduced in the 19th century, and has been extensively studied since then. Most textbooks in economics treat simplified cases only, with 2 or 3 firms competing for the market. For the general case, some simple situations have been treated in [6] and [2]. Here we show how the use of linear algebra in a level above undergraduate courses can lead to the description of long term behavior for the more general situations. Several modelling issues are considered such as discrete or continuous time periods and constant or linear marginal costs.