Cournot Duopoly Model Research Articles

Predation in Off-Patent Drug Markets

In 2009, Sanofi-Aventis, whose generic subsidiary is Winthrop, merges with the generic firm, Zentiva. This paper fills the gap in the theoretical literature concerning mergers in pharmaceutical markets. To prevent generic firms from increasing their market share, some brand-name firms produce generics themselves, called pseudo-generics. We develop a Cournot duopoly model by considering the pseudo-generics production as a mergers’ catalyst. We show that a brand-name company always has an incentive to purchase its competitor. The key insight of this paper is that the brand-name laboratory can increase its merger gain by producing pseudo-generics beforehand. In some cases, pseudo-generics would not otherwise be produced and this production is then a predatory strategy.

Detecting chaos in a duopoly model via symbolic dynamics

This paper considers a Cournot duopoly model assuming isoelastic demand and smooth cost functions with built-in capacity limits. When the firms cannot obtain positive profits they are assumed to choose small stand-by outputs rather than closing down, in order to avoid substantial fitting up costs when market conditions turn out more favorable. It is shown that the model provides chaotic behavior. In particular, the system has positive topological entropy and hence the map is chaotic in the Li-Yorke sense. Moreover, chaos is not only topological but also physically observable.

DECISION MAKING ON STRATEGIC ENVIRONMENTAL TECHNOLOGY LICENSING: FIXED-FEE VERSUS ROYALTY LICENSING METHODS

Because of a deterioration in the quality of the environment, this paper studies the effects of the environment and the economy on environmental technology licensing in a homogeneous Cournot duopoly model in order to reduce environmental pollution and hence improve social welfare. To this end, two licensing methods — namely, a fixed-fee licensing method and a royalty licensing method — are compared. It is found that a high emission tax rate induces the innovator to not license the environmental technology to the licensee under the fixed-fee licensing method. As for social welfare, a large innovation scale of environmental technology does not guarantee that social welfare will be maximized. Finally, a large innovation scale of environmental technology is likely to increase consumer surplus if the marginal environmental damage is significant. Consumers are likely to prefer royalty licensing to fixed-fee licensing. This conclusion differs from Wang's finding in 2002.

Bifurcation analysis of a dynamic duopoly model with heterogeneous costs and behavioural rules

We develop a nonlinear dynamic Cournot duopoly model in discrete time, where two bounded rational quantity-setting firms, both endowed with naïve expectations, are heterogeneous as to their cost functions and output strategies. One of the two competing firms adopts best-reply behaviour, whereas the other adjusts its production according to the gradient of its profit. Although excessive reaction of the latter firm generally results in destabilization of the ‘Cournot–Nash’ equilibrium and brings about complex dynamic scenarios, this occurs via qualitatively different bifurcation routes, depending on the ratio between firms’ marginal costs. The paper also provides a preliminary exploration of the long-run sustainability of the heterogeneous duopoly competition, by investigating numerically the impact of fixed costs on firms’ survival, along different output trajectories.

Higher-codimension bifurcations caused by delay

In this paper, we give a detailed study of rich dynamics in two-parameter families of two-dimensional generalized delayed discrete Cournot duopoly models. Multistability, such as the coexistence of period-2/quasiperiodic (limit-cycle), chaotic/regular motions or synchronized/asynchronized solutions are discussed. Complexity caused by delay, including the change of local stability regions and the occurrence of higher-codimension bifurcations, is to be discovered.

Are Partial Ownership Arrangements Advantageous ?

Using a two-stage differentiated-product Cournot duopoly model with technological spillovers, this paper investigates the effect partial ownership arrangements (POAs) among rivals has on the market outcome when firms also compete in a non-production activity, RqD. Although POAs are found to be associated with lower profits, when the degree of product differentiation is small and technological spillovers are relatively large, they are found to result in higher RqD, output and social welfare levels.JEL Classification: D43, L13, L15

On the Optimality of Escalated Tariff Structure: A Cournot Duopoly Analysis

This paper examines whether an escalated tariff structure will maximize national welfare by using a simple Cournot duopoly model, where an intermediate good and a final good are vertically related. In this paper, some general results are derived. It is shown that the escalated tariff structure prevailing in most countries does not necessarily benefit an importing country more than a de-escalated tariff structure. The condition for an importing country to adopt an escalated tariff structure is a huge loss incurred by a domestic final-good producer resulting from a tariff imposed on imports of the intermediate good. A de-escalated tariff structure should be adopted by an importing country as a tariff on imports of the final good harms the domestic consumers much more than a tariff on imports of the intermediate good.

Multistability and complex dynamics in a simple discrete economic model

In this paper, we will propose a generalized Cournot duopoly model with Z 2 symmetry. We demonstrate that cost functions incorporating an interfirm externality lead to a system of couple one-dimensional maps. In the situation where agents take turns, we find in an analytic way that there coexist multiple unstable/stable period-2 cycles or synchronized/asynchronized periodic orbits. Coupling one-dimension chaos can be observed. In a more general situation, where agents move simultaneously, a closer analysis reveals some well-known local bifurcations and global bifurcations which typically occur in two-parameter families of two-dimensional discrete time dynamical systems, including codimension-one (fold-, flip-, Neimark–Sacker-) bifurcations, codimension-two (fold/flip, 1:2 resonance, 1:3 resonance and 1:4 resonance) bifurcations, and hetero-clinic, homo-clinic bifurcations, etc. Multistability, including the coexistence of synchronized/asynchronized solutions are also discussed.

When does grey market occur? A Cournot duopoly model of intrabrand competition

Grey markets have troubled international businesses for many years. The main suppliers of grey-market goods are diverters, who obtain brand-owner's authorisation at one country and sells branded goods to a grey marketer at another country in which they are not authorised. This paper proposes a duopoly model that takes the diverter's point of view to answer the unsolved questions in grey marketing. The equilibrium solution is obtained by Cournot assumption, which assumes that each firm acts independently and attempts to maximise its profits by choosing its output. The extension and implications of this model are also discussed.

Cournot Duopoly with competition in the R&D expenditures

AbstractWe present a new R&D investment in a Cournot Duopoly model and we analyze the different possible types of Nash R&D investments. We observe that the new production costs region can be decomposed in three economical regions, depending on the Nash R&D investment, showing the relevance of the use of patents in new technologies. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Capital Structure and Entry Deterrence with Multiple Incumbents

Abstract This paper uses a two-stage Cournot duopoly model with demand uncertainly to examine the strategic role debt plays in deterring a company from entering when a potential entrant can enter one of several markets. We show that as the number of alternative markets available for entry rises, the incumbents' incentive to use debt as a deterrent falls. Thus, a potential entrant will prefer to have a larger number of alternative markets to enter in order to lower the incumbents' incentive to take strategic actions against it.

Entry Deterrence in a Duopoly Market

Abstract In a homogeneous good, Cournot duopoly model, entry may occur even when the potential entrant has no cost advantage and no independent access to distribution. By sinking its costs of production before negotiating with the incumbents, the entrant creates an externality that induces the incumbents to bid more aggressively for the distribution rights to its output. Each incumbent is willing to pay up to the incremental profit earned from the additional output plus the incremental loss avoided by keeping the output away from its rival. This implies that the incumbents are willing to pay up to the market price for each unit of available output. A sequential game in which the incumbents produce first is analyzed, and the conditions under which entry is deterred by incumbents' preemptive capacity expansions are derived.

Stable cycles in a Cournot duopoly model of Kopel

We consider a discrete map proposed by M. Kopel that models a nonlinear Cournot duopoly consisting of a market structure between the two opposite cases of monopoly and competition. The stability of the fixed points of the discrete dynamical system is analyzed. Synchronization of two dynamics parameters of the Cournot duopoly is considered in the computation of stability boundaries formed by parts of codim-1 bifurcation curves. We discover more on the dynamics of the map by computing numerically the critical normal form coefficients of all codim-1 and codim-2 bifurcation points and computing the associated two-parameter codim-1 curves rooted in some codim-2 points. It enables us to compute the stability domains of the low-order iterates of the map. We concentrate in particular on the second, third and fourth iterates and their relation to the period doubling, 1:3 and 1:4 resonant Neimark–Sacker points.

Nonlinear Cournot Duopoly Model : Under Cubic Cost Functions with a Negative Externality and Differences in Production Costs

We consider the Cournot duopoly model under the assumption that cost functions are a cubic function of own and competitors' outputs. Therefore, we incorporated a negative external effect into cost functions because cost functions lead to non-monotonic, in particular unimodal reaction functions. The shape of the reaction curve is the same as the Puu [5] model. The number and the stability of the Nash-equilibrium depend on the degree of external effect and the differences in the coefficients of the cost functions. If there exists no differences in the coefficients, the three Nash-equilibria increase the degree of external effects, and the adjustment fails to converge to any equilibria. If there exists differences in the coefficients, the number of equilibria decrease in some cases, but do not always mean stabilization of the Nash-equilibrium. The Nash-equilibrium becomes unstable again when the differences expand. If there exist differences in the coefficients, a general cubic equation must be solved to result in the Nash-equilibrium. The shape of the solutions is algebraically complex, because they have a cube root. The stability of the Nash-equilibrium is explained by graphical methods. In the graphical methods, the boundaries that result in the the discriminant solutions becoming zero to provide some information.JEL Classification: C63, D21, D43

Rural Internet access: over‐subscription strategies, regulation and equilibrium

AbstractThis paper presents an analysis of the Internet access market using a game theoretic model. In particular, we consider the Nash equilibrium of the service providers and examine their behavior on network investment and output level. We calibrate this model to fit the industry structure and data found in rural markets. In the first part of the paper, we examine the Internet industry structure and its characteristics. Based on the industry structure, we create a Cournot duopoly model, in which real world cost and revenue projections are used to find Internet access market equilibrium. In conclusion, we analyze social welfare of the equilibrium. These analyses allow us to explain the motivation for the rural ISPs' behavior, such as over‐subscription and under‐investment and to present an analytical framework for Internet industry policy makers. Copyright © 2007 John Wiley & Sons, Ltd.

Multinational Production, Absorptive Capacity, and Endogenous R&D Spillovers

AbstractDo R&D spillovers have an impact on whether firms choose to go multinational or not? We present a three‐stage Cournot duopoly model, which identifies under what conditions firms choose to service a foreign market through exports or localized production. The establishment of a foreign subsidiary improves the ability to learn from foreign R&D since spillovers are strongly moderated by geographical distance. We explicitly model the concept of absorptive capacity, where gains from spillovers are determined by own R&D investments. With exogenous R&D investments, the absorptive capacity effect contributes to increase the gains from going multinational when the firm is R&D‐intensive. However, if R&D investments are endogenous, only medium‐sized absorptive capacity effects will result in firms going multinational. Furthermore, higher spillover rates do not necessarily drive down R&D and profits for the multinational firm. This stands in contrast to models that ignore absorptive capacity effects.

Controlling the Cournot-Nash Chaos

The recently developing theory of nonlinear dynamics shows that any economic model can generate a complex dynamics involving chaos if the nonlinearities become strong enough. This study constructs a nonlinear Cournot duopoly model, reveals conditions for the occurrence of chaos, and then considers how to control chaos. The main purpose of this paper is to demonstrate that chaos generated in Cournot competition is in a double bind from the long-run perspective: a firm with a lower marginal production cost prefers a stable (i.e., controlled) market to a chaotic (i.e., uncontrolled) market, while a firm with a higher marginal cost prefers the chaotic market.

Export subsidies, countervailing duties, and welfare

Using a simple Cournot duopoly model, this paper provides an important policy implication for trade disputes involving export subsidies. In this paper, the possibility that a foreign export subsidy could benefit the domestic country as well as the foreign country by appropriately using countervailing duties is identified.

Market structure and insider trading

In this paper we examine the real and financial effects of two insiders trading in a static Jain and Mirman model [Jain, N., & Mirman, L. J. (2000). Real and financial effects of insider trading with correlated signals. Economic Theory, 16, 333–353] (henceforth JM). The first insider is the manager of the firm. The second insider is the owner. First, we study the change of the linear-equilibrium variables, in the presence of two insiders. Specifically, we show that the trading order and the real output of the manager are less in this model than in JM model [Jain, N., & Mirman, L. J. (2000). Real and financial effects of insider trading with correlated signals. Economic Theory, 16, 333–353]. Secondly, we show that the stock price reveals more information than in Cournot duopoly and monopoly models studied by Jain and Mirman [Jain, N., & Mirman, L. J. (2000). Real and financial effects of insider trading with correlated signals. Economic Theory, 16, 333–353; Jain, N., & Mirman, L. J. (2002). Effects of insider trading under different market structures. The Quarterly Review of Economics and Finance, 42, 19–39]. Finally, we analyze the comparative statics (insiders' profits) of this model, when the market maker receives one or two signals.

Basins of attraction in a Cournot duopoly model of Kopel

For a nonlinear Cournot duopoly map of Kopel, we show that a circle, lines, and rectangles play a key role in determining the basins of attraction in the case of three nontrivial Nash equilibria.