Cournot Duopoly Model Research Articles

The government regulation and market behavior of the new energy automotive industry

Environmental issues and cleaner production are getting increasing attentions currently, making the clean production and sustainable consumption with low emissions significant. Traditional energy vehicles are increasingly unsuitable for the development of current society. It's a trend in the current vehicle market to accelerate the substitution of new energy vehicles for traditional energy vehicles. This paper makes a theoretical study on the development of new energy vehicle market supported by the government. First, this paper establishes a Cournot duopoly model which includes domestic and imported new energy vehicle manufacturers. Through the analysis of this model, this paper argues that government support policies such as subsidies and tariffs can effectively expand the market share of domestic new energy vehicles with less technology. Yet this approach is unsustainable, because domestic new energy vehicles with less technology can only survive in the market by shortening the gap with imported brands. Secondly, this paper establishes a Stackelberg model with product price as the decision variable and find that when there is a technical gap, the first mover advantage in the market will no longer exist. Finally, this paper compares two kinds of subsidies for domestic new energy vehicles and shows that the two subsidies are not different from subsidizing consumers or enterprises in expanding market share, and the consumer can obtain higher social welfare level as the subsidy object.

The optimal technology licensing strategy under supply disruption

We study the problem of whether and how a patent-holding firm (supplier S1) should license its technology patent to a potential rival (supplier S2). If the license is given, the two suppliers both produce a critical component for their downstream manufacturer simultaneously (sequentially) when the manufacturer adopts a dual (contingent) sourcing mode. However, both suppliers face risks of complete supply disruptions. In the study, we examine how the supply risk affects S1's technology licensing willingness and under which conditions royalty or fixed-fee licensing is its optimal strategy. The results show that when the manufacturer adopts contingent sourcing, S1 is always willing to license its technology to S2 and fixed-fee licensing is the optimal strategy. However, when dual sourcing is adopted, either royalty and fixed-fee licensing could be S1's optimal licensing strategy, depending on the reliability degree of the suppliers’ productions. Our findings extend the conclusion from previous researchers about royalty and fixed-fee licensing in a Cournot duopoly model.

Delay Cournot duopoly models revisited.

In considering economic dynamics, it has been known that time delays are inherent in economic phenomena and could be crucial sources for oscillatory behavior. The main aim of this study is to shed light on what effects the delays can generate. To this end, different models of Cournot duopoly with different delays are built in a continuous time framework and their local and global dynamics are analytically and numerically examined. Three major findings are obtained. First, the stability switching conditions are analytically constructed. Second, it is numerically demonstrated that different lengths of the delays are sources for the birth of simple and complicated dynamics. Third, the delay for collecting information on the competitors' output alone does not affect stability.

Patent protection and R&D investment in a differentiated cournot duopoly with technology licensing

In this paper, we develop a differentiated Cournot duopoly model to investigate the impact of patent protection on a firm’s R&D investment in the presence of two-part tariff licensing. The result shows that the innovator’s R&D investment can be maximized at an intermediate patent protection under two-part tariff licensing, whereas it is always maximized at the strongest patent protection without licensing. Furthermore, the result also demonstrates that two-part tariff licensing can lead to an increase in social welfare, regardless of the degree of patent protection taken by the innovator, but whether it can increase the innovator’s R&D investment mainly depends on its R&D efficiency and product differentiation of the two firms

Nonlinear Phenomena in Cournot Duopoly Model

The economic world is very dynamic, and most phenomena appearing in this world are mutually interconnected. These connections may result in the emergence of nonlinear relationships among economic agents. Research discussions about different markets’ structures cannot be considered as finished yet. Even such a well-known concept as oligopoly can be described with different models applying diverse assumptions and using various values of parameters; for example, the Cournot duopoly game, Bertrand duopoly game or Stackelberg duopoly game can be and are used. These models usually assume linear functions and make analyses of the behavior of the two companies. The aim of this paper is to consider a nonlinear inverse demand function in the Cournot duopoly model. Supposing there is a sufficiently large proportion among the costs of the two companies, we can possibly detect nonlinear phenomena such as bifurcation of limit values of production or deterministic chaos. To prove a sensitive dependence on the initial condition, which accompanies deterministic chaos, the concept of Lyapunov exponents is used. We also point out the fact that even though some particular values of parameters are irrelevant for the above-mentioned nonlinear phenomena, it is worth being aware of their existence.

Optimal licensing schemes for a mixed ownership firm when facing uncertain R&D outcomes and technology spillover

In this paper, we develop a mixed Cournot duopoly model to investigate whether and how a mixed ownership firm licenses its non-drastic innovation to the private rival when facing uncertain R&D outcomes and technology spillover. The results show that, (i) in terms of fixed-fee and royalty licensing, the optimal licensing contract is always the fixed-fee when the private share is low, while it is always the royalty when both the private share and product substitutability are sufficiently high. As for other cases, whether the fixed-fee is superior to the royalty also depends on the degree of technology spillover; and (ii) even if the two-part tariff is available for the mixed firm, the fixed-fee alone is still one possible form of the optimal licensing contract. Moreover, the finding also shows that the probability of R&D success plays a critical role in the process of determining the licensing strategy for the mixed firm.

The stability of Bayesian Nash equilibrium of dynamic Cournot duopoly model with asymmetric information

Few literatures apply complex oligopoly dynamics theory in games of incomplete information. This paper aims at analyzing dynamic behaviors of Bayesian game. A dynamic Cournot model with asymmetric information is proposed based on adaptive expectation and bounded rationality. Theoretical analysis draws two important conclusions: firstly, Bayesian Nash equilibrium of dynamic Cournot duopoly model with two players of adaptive expectation is always globally asymptotically stable. Secondly, Bayesian Nash equilibrium of dynamic Cournot duopoly model with players of adaptive expectation and gradient rule based on marginal profit is locally asymptotically stable only when parameters satisfy certain conditions. In our model, a firm of uncertain cost function is designed. A probability parameter θ of private type which differentiates high cost and low cost is introduced. Bifurcation, or even chaos with respect to θ, is performed by simulation which implies that large possibility of high-cost production yields easier chaos in duopoly market. High adjustment speeds of output form a three-dimensional strange attractors region. The unstable system's negative impact on equilibrium output and profit highlights the importance of system stability. Chaos control is in order to stabilize the equilibrium of the improved dynamic Cournot model with asymmetric information.

Taxation and the sustainability of collusion: ad valorem versus specific taxes

Assuming constant marginal cost, it is shown that a switch from specific to ad valorem taxation that results in the same collusive price has no effect on the critical discount factor required to sustain collusion. This result is shown to hold for Cournot oligopoly when collusion is sustained with Nash-reversion strategies or optimal-punishment strategies. In a Cournot duopoly model with linear demand and quadratic costs, it is shown that the critical discount factor is lower with an ad valorem tax than with a specific tax that results in the same collusive price. However, in contrast to Colombo and Labrecciosa (J Public Econ 97:196–205, 2013) it is shown that the revenue is always higher with an ad valorem tax than with a specific tax.

Conjectures between Two Cournot Firms with Symmetric Information and Their Risk-taking Behaviours

This paper introduces the simple and standard Cournot duopoly model in a symmetric situation in which each firm has the same information on the cost function of its rival. This paper considers two types of firms’ risk-taking behaviours and two classes of symmetric information. First, we consider that both firms are risk neutral and have perfect information. In this case, we obtain a unique Cournot equilibrium. Second, when both firms are risk neutral and have partial information, that is, each firm’s set of information changes from perfect to partial information, the number of equilibrium changes from one to four compared to case 1. Third, when both firms are risk averse and have perfect information, that is, firms’ risk taking behaviours change from risk neutral to risk averse, the number of equilibrium changes from one to three compared to case 1. Therefore, both firms’ information structure and risk taking behaviours affect their optimal output strategies.

Robust games: theory and application to a Cournot duopoly model

In this paper, the robust game model proposed by Aghassi and Bertsimas (Math Program Ser B 107:231–273, 2006) for matrix games is extended to games with a broader class of payoff functions. This is a distribution-free model of incomplete information for finite games where players adopt a robust-optimization approach to contend with payoff uncertainty. They are called robust players and seek the maximum guaranteed payoff given the strategy of the others. Consistently with this decision criterion, a set of strategies is an equilibrium, robust-optimization equilibrium, if each player’s strategy is a best response to the other player’s strategies, under the worst-case scenarios. The aim of the paper is twofold. In the first part, we provide robust-optimization equilibrium’s existence result for a quite general class of games and we prove that it exists a suitable value $$\epsilon $$ such that robust-optimization equilibria are a subset of $$\epsilon $$ -Nash equilibria of the nominal version, i.e., without uncertainty, of the robust game. This provides a theoretical motivation for the robust approach, as it provides new insight and a rational agent motivation for $$\epsilon $$ -Nash equilibrium. In the last part, we propose an application of the theory to a classical Cournot duopoly model which shows significant differences between the robust game and its nominal version.

A heterogenous Cournot duopoly with delay dynamics: Hopf bifurcations and stability switching curves

This article considers a Cournot duopoly model in a continuous-time framework and analyze its dynamic behavior when the competitors are heterogeneous in determining their output decision. Specifically the model is expressed in the form of differential equations with discrete delays. The stability conditions of the unique Nash equilibrium of the system are determined and the emergence of Hopf bifurcations is shown. Applying some recent mathematical techniques (stability switching curves) and performing numerical simulations, the paper confirms how different time delays affect the stability of the economy.

Profit-sharing licensing

Profit-sharing licensing is quite a common business practice. In a Cournot duopoly model, we showed that if not subject to any restrictions this kind of technology for equity deal would lead to a decline in industry output and hurt consumers. To avoid the industry output contraction and protect the interests of consumers, the government can intervene in licensing by requiring that the profit-sharing rate specified by a licensing contract should not exceed the percentage difference of involved firms’ equilibrium outputs before licensing.

Corporate social responsibility in a game-theoretic context

Using a simple Cournot duopoly model with differentiated products, this work studies the firms’ strategic choice of whether to adopt Corporate Social Responsibility (CSR) rules. The proposed game-theoretic approach shows that, depending on the degree of product differentiation and firms’ social concern, different equilibria arise: (1) all firms in the industry follow CSR rules, (2) all firms are profit-maximising (PM), (3) asymmetric equilibria are present (one CSR firm, one PM firm), and (4) multiple symmetric equilibria are present. Under Bertrand competition, universal PM is the unique equilibrium in which the social welfare is the least desirable: this implies that, in contrast to the conventional wisdom, Bertrand may appear as welfare dominated by Cournot. This work can help to explain the widely observed phenomenon, in the real world, of different industries in which firms’ CSR behaviours are more or less commonly widespread.

Quantity and collection decisions in a closed-loop supply chain with technology licensing

Industry practice has shown that technology licensing has an important effect on the remanufacturing of patented products by third parties. Different licensing methods significantly impact a supply chain member's production and collection decisions, and they also have influential effects on reverse channel performance. However, there is scant literature investigating the decision on technology licensing and its impact on a supply chain member's production and collection decisions. To address this gap, we consider a manufacturer, as the patent holder, who produces new and remanufactured products and, simultaneously, he and a remanufacturer (as the licensee, who by law can only produce remanufactured products) competitively collects used products from the market in a two-period closed-loop supply chain (CLSC). We investigate two licensing patterns, fixed fee versus royalty, within the CLSC in a Cournot duopoly model. We find that royalty licensing is dominated by fixed fee licensing from the viewpoints of both the consumer surplus and environmental protection. Our result also shows that the manufacturer's optimal licensing strategy is determined by a threshold of the fixed fee: when the fixed fee is below a threshold, it is better for the manufacturer to use a royalty licensing, whereas fixed-fee licensing should be used when the fixed fee is higher than a threshold.

Passive Unilateral Cross-ownership and Strategic Trade Policy

Abstract In a Cournot duopoly model in which exporters compete in a third market, this paper revisits the classical issue (dating back to the pioneering work of Brander and Spencer, Export Subsidies and International Market Share Rivalry, 1985) of the strategic trade policy choice in the presence of the passive participation of one firm in the rival. Passive cross-ownership dramatically alters the participating and participated firms’ governments’ choice to apply the strategic trade policy instrument, the equilibria typology and their efficiency properties. In fact, if the share of cross-ownership is sufficiently large, the participated firm’s government finds optimal to tax export. Moreover, beyond an adequately high threshold, cross-ownership modifies the equilibrium from the activist regime for both countries to an asymmetric regime in which only the participating firm’s government intervenes. In addition, in the case of the traditional common activist regime equilibrium, the classical prisoner’s dilemma game structure may disappear.

Dynamical analysis of a Cournot duopoly model

Abstract In this paper, two different mechanisms are used to study a homogeneous Cournot duopoly in a market characterized by the downward sloping and concave price function. Two firms, which have constant marginal costs, use adaptive, low-rationality mechanisms to adjust their production levels toward equilibrium. In particular, the stability of the equilibrium for two different mechanisms is studied. However, complex dynamics arise, especially when the reaction coefficient increases. Finally, we compare the obtained results of the two models.

Tariffs, technology licensing and adoption

This paper develops a two-country Cournot duopoly model to investigate the implications of international technology licensing. It is shown that if the tariff imposed by the domestic country is high, it is optimal for the foreign firm to adopt an inferior technology for its production when it licenses its most advanced technology to the domestic firm. Such a licensing arrangement may improve welfare of the two countries.

Licensing strategy for a stochastic R&D firm in a differentiated Cournot duopoly model

This paper investigates an innovating firm’s licensing strategy in a differentiated Cournot duopoly model when the firm is an insider and the R&D outcome is stochastic. We develop a duopoly game model in which the innovating firm has three options for licensing its innovation: fixed-fee licensing, royalty licensing and two-part tariff licensing. We consider three stages in the model: the R&D, licensing and output stages. We find that product differentiation and technology spillover play significant roles in the innovating firm’s choice between fixed-fee and royalty licensing. In addition, regardless of the degree of product differentiation, we find that (1) two-part tariff licensing is superior to both fixed-fee and royalty licensing when technology spillover is low and that (2) two-part tariff licensing is equivalent to royalty licensing when technology spillover is high.DOI: http://dx.doi.org/10.5755/j01.ee.26.5.12313

배출권 할당 및 회계처리 방식이 기업의 시장 지위에 미치는 영향

According to Law on Allocation and Trading of GHG Allowances of 2013 in Korea as well as the 2014 National Master Plan for Korean Emissions Trading System, the System should be designed to minimize the change in the market positions of the affected firms. In this paper, we investigate how that principle might become ineffective by the ways of distributing allowances and applying different accounting methods using a Cournot duopoly model. Although the way of allocating allowances freely to firms combined with accounting them for having no values would minimize their market positions, it would not the most cost-effective way of GHG reduction since it does not provide financial market with accurate informations.

Delay dynamics of a Cournot game with heterogeneous duopolies

We construct a Cournot duopoly model in a continuous-time framework and consider its dynamic behavior when the firms are heterogeneous in determining their output decision: one firm has an information delay in the competitor’s output as well as an implementation delay in its own output while the other firm does not have any delays. Two main results are obtained. One is that the information delay does not affect dynamics of the commodities and the other is that the implementation delay can destabilize the otherwise stable equilibrium. Furthermore, it is numerically confirmed that the two delay duopoly model can generate a wide spectrum of dynamics ranging from cyclic dynamics to chaos.