Accreditation in a differentiated duopoly

Accreditation is increasingly important worldwide; however, some industries have higher accreditation rates than others. We suggest a duopoly model to discuss how market characteristics affect the incentive for firms to seek accreditation. The discussion relates to the effects accreditation might have on the costs and demands in the markets, the degree of product differentiation (addressing both substitutable and complementary goods), type of competition (various Cournot and Bertrand games), and welfare for society. It follows that markets with high accreditation rates are either characterized by fierce competition (price competition in substitutable goods) or by a high degree of coordination (complementarity).     

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.     

Environmental taxes in a differentiated mixed duopoly

Beladi and Chao (2006) and Bárcena-Ruiz and Garzón (2006) considered the role of environmental policy on the decision whether to privatize a public firm in different market structures. This paper re-examines whether privatization improves (or deteriorates) the environment in a mixed duopolistic framework with differentiated product and pollution abatement. It is shown that, due to privatization, less attention is paid to pollution abatement by all the firms coupled with less environment taxes levied by the government in a differentiated duopoly, and the environment is more (less) damaged when the product is less (more) substitutable. When the product is highly substitutable, industry profits increase because this softens the intensity of the product market, but social welfare deteriorates accompanied with the path of privatization because the loss of consumer surplus and tax revenue exceeds the increases in profits, even if the environment is less damaged.     

Cournot duopoly and insider trading with two insiders

We study the effect of competition among insiders in an extension of the static Kyle [Kyle, A. (1985). Continuous auctions and insider trading. Econometrica, 53, 1315–1335] model of insider trading introduced by Jain and Mirman (JMC) [Jain, N., & Mirman, L.J. (2002). Effects of insider trading under different market structures. The Quarterly Review of Economics and Finance, 42, 19–39]. In the JMC model competition in the real sector is introduced. In this paper we introduce competition in the stock sector in the JMC model by assuming that there is a manager who is responsible for making the real decisions of the firm as well as an ‘owner’ who has the same information as the manager but has no managerial responsibilities. In this way we can study the interaction between competition in the real sector and competition in the financial sector. We show that the stock price set by the market makers reveals more information than in the JMC model and that the expected equilibrium values of the manager’s profits sometimes decline and sometimes increase depending on the exogenous parameters of the model. Moreover, we prove that due to the competition in the financial sector, the level of output produced by the firm is less than in JMC. Finally, we also study the effect of financial competition in the case in which the market makers receive only one signal and analyze the comparative statics in this case.     

Environmental R&D and privatization in a mixed duopoly market

The study examines strategic environmental research and development (ER&D) under environmental tax in a mixed duopoly and further analyzes the impact of privatization on it. We show that the environmental tax may not necessarily promote the private (or public) firm's ER&D, and the relative ER&D performance between firms depends on the public firm's environmental attitudes and the tax rate. When the public firm cares much for environment, it can be used as an instrument to correct the private firm's underinvestment (or overinvestment) in ER&D. Moreover, privatization can (cannot) raise both firms' ER&D simultaneously if the tax rate is high (low).     

Spatial discrimination: Bertrand vs. Cournot with asymmetric demands

This paper develops a barbell model a la Hwang and Mai [Hwang, H., and C.C. Mai, 1990, Effects of spatial price discrimination on output, welfare, and location, American Economic Review 80, 567–575.] with homogeneous product and asymmetric demands to compare prices, aggregate profits and social welfare between Cournot and Bertrand competition, and to analyze the firms' equilibrium locations. It focuses on the impacts of the spatial barrier generated from transport costs, and the market size effect resulting from asymmetric demands. It shows that the market-size effect is crucial in determining firms' locations under Cournot competition, but insignificant under Bertrand competition. Moreover, the equilibrium price of the large market and the aggregate profits are lower but the social welfare is higher under Cournot competition than under Bertrand competition if one of the markets is sufficiently large and the transport cost is high.     

Endogenous spillovers in a non-tournament R&D duopoly under uncertainty

Including R&D risk, this paper considers the choices of R&D spillovers in a simple non-tournament cost-reducing R&D duopoly game with Bertrand competition. It turns out that the two firms never disclose any of their R&D information when considering their R&D non-cooperatively. However, if the firms decide their R&D cooperatively, we show, though they would always fully share their information when the risk of R&D is low, they would not disclose any of their R&D information when the market competition is fierce, the R&D risk is high and the R&D is efficient.     

Differentiated goods in a dynamic Cournot duopoly with emission charges on output

We extend the dynamic Cournot duopoly framework with emission charges on output by Mamada and Perrings (Econ Anal Policy 66:370–380, 2020), which encompassed homogeneous products in its original formulation, to the more general case of differentiated goods, in order to highlight the richness in its static and dynamic outcomes. Each firm is taxed proportionally to its own emission only and charge functions are quadratic. Moreover, due to an adjustment capacity constraint, firms partially modify their output level toward the best response. Like in Mamada and Perrings (Econ Anal Policy 66:370–380, 2020), the only steady state coincides with the Nash equilibrium, and it will be considered admissible when it guarantees the positivity of the marginal emission charge. We find that the full efficacy of the environmental policy, which applies to an equilibrium that is globally asymptotically stable anytime it is admissible, is achieved in the case of independent goods, as well as with a low good interdependence degree in absolute value, independently of being substitutes or complements. When goods are substitutes and their interdependence degree is high, the considered environmental policy is still able to reduce pollution at the equilibrium, but the latter is stable just when the policy intensity degree is large enough. When instead goods are complements and their interdependence degree is high in absolute value, the considered environmental policy produces detrimental effects on the pollution level and the unique equilibrium is always unstable, when admissible. This highlights that, from the static viewpoint, even in the absence of free riding possibilities, the choice of the mechanism to implement has to be carefully pondered, according to the features of the considered economy.

     

Heterogeneous players in a Cournot model with differentiated products

In this article, we analyse a duopolistic Cournotian game with firms producing differentiated goods, marginal costs are constant and demand functions are microfounded. We consider firms adopting different decisional mechanisms which are based on a reduced degree of rationality. In particular, we assume that a firm adopts the local monopolistic approximation approach, while the rival adjusts its output level according to the gradient rule. We provide conditions for the stability of the Nash equilibrium and investigate some bifurcation scenarios as parameters vary. The main finding of the article is that both a high level and a low level in goods differentiation may have a destabilising role in the system.     

Correlated equilibria in homogeneous good Bertrand competition

We show that there is a unique correlated equilibrium, identical to the unique Nash equilibrium, in the classic Bertrand oligopoly model with homogeneous goods and identical marginal costs. This provides a theoretical underpinning for the so-called “Bertrand paradox” as well as its most general formulation to date. Our proof generalizes to asymmetric marginal costs and arbitrarily many players in the following way: The market price cannot be higher than the second lowest marginal cost in any correlated equilibrium.     

Strategic pricing of differentiated consumer durables in a dynamic duopoly: A numerical analysis

Under different modes of competitive pricing behavior, profit-maximizing price trajectories are derived for durable products in a dynamic duopoly. Open-loop co-operative and non-cooperative pricing behavior is analyzed within a comprehensive model where sales of differentiated products are described by interlocked diffusion processes with realistic demand characteristics. Because of analytic complexity, the optimal trajectories implied by the control and differential-game problems are derived numerically across an extensive set of plausible market scenarios. Manipulation of initial market conditions enables derivation of optimal competitive pricing as a function of timing of entry.     

Endogenous managerial incentive contracts in a differentiated duopoly,with and without commitment

In a differentiated Cournot duopoly, we examine the contracts that firms' owners use to compensate their managers and the resulting output levels, profits and social welfare. If products are either sufficiently differentiated or sufficiently close substitutes, owners use Relative Performance contracts. For intermediate levels of product substitutability, they use Market Share contracts. When owners do not commit over the types of contracts, each type is an owner's best response to his rival's choice. Product substitutability has differential effects on output levels and profits, depending on the configuration of contracts in the industry. Finally, managerial incentive contracts are welfare enhancing if they increase consumers' surplus. Copyright © 2010 John Wiley & Sons, Ltd.     

Learning cycles in Bertrand competition with differentiated commodities and competing learning rules

This paper stresses the importance of heterogeneity in learning. We consider a Bertrand oligopoly with firms using either least squares learning or gradient learning for determining the price. We demonstrate that convergence properties of the rules are strongly affected by heterogeneity. In particular, gradient learning may become unstable as the number of gradient learners increases. Endogenous choice between the learning rules may induce cyclical switching. Stable gradient learning gives higher average profit than least squares learning, making firms switch to gradient learning. This can destabilize gradient learning which, because of decreasing profits, makes firms switch back to least squares learning.     

基于cournot Model与Bertrand Model寡头竞争模型的药品最优定价策略

本文将竞争博弈模型引用到药品定价策略中,分别从制造商利润最大化,销售商利润最大化以及总体药品市场价值最大化的角度,研究了在Cournot Model下,制造商应该对销售商采取如何定价策略,而销售商应该如何应对才能达到总体利润最大化;在Bertrand Model下,论证多个药品制造商应该采取一体化的价格管理体系,并在文章最后给出Cournot Model以及Bertrand Model的寡头竞争模型在药品流通渠道管理中的应用。     

On the non-existence of equilibria in differentiated product models

It is sometimes suggested that the non-existence of an equilibrium in the Hotelling spatial model pointed out by d'Aspremont, Gabszewicz and Thisse (1979) is due to demand discontinuity. In this paper we first show that demand continuity is a natural property in general spatial or differential product markets. However, we also claim that the non-existence of an equilibrium is also a general property of these models. Further the assumption of no mill-price undercutting suggested by Eaton and Lipsey (1978) and Novshek (1980) is shown to be not sufficient to restore existence.     

Rebates in a Bertrand game

We study a price competition game in which customers are heterogeneous in the rebates they get from either of two firms. We characterize the transition between competitive pricing (without rebates), mixed strategy equilibrium (for intermediate rebates), and monopoly pricing (for larger rebates).     

On the non-existence of oligopolistic equilibria in differentiated products spaces

In a large class of product differentiation models á la Hotelling, the firms' payoffs in the game involving location in the differentiated products space exclusively depends on the distance to their neighbouring firms, rather than on the firms' locations proper. This leads to a degeneracy on the firms' strategy space. Using alternative equilibrium concepts, this is shown to be the reason for the non-existence of non-cooperative equilibria, especially if the firms' technologies are not identical.     

Spatial Cournot competition and economic welfare: a note

We investigated welfare implications in location-quantity models in a symmetric linear city. We found that when firms are not agglomerated in equilibrium, increasing the distance between firms raises (reduces) producer surplus and social welfare (consumer surplus). Moreover, central agglomeration is always optimal for consumers among symmetric locations, but not necessarily for producers. Central agglomeration can be inefficient even if it is the unique equilibrium outcome. In short, the firms are more likely to agglomerate or locate closer than what welfare maximizers would dictate, whereas they locate farther apart than what consumer surplus maximizers would recommend.