Oligopoly and stability

In this paper, the so called Theocharis–Cournot problem is reconsidered. It concerns the relation between oligopoly and perfect competition, in particular the destabilization of Cournot equilibrium when the number of competitors increases. Using a CES production function where one input, capital, is fixed during periods of investment, a mixed short/long run market dynamics is set up. In the short run, with capital fixed, there is a capacity limit for production possibilities, whereas, at moments of capital renewal there are constant returns to scale. In this setting the local stability of Cournot equilibrium is reconsidered. It is demonstrated that if no more than two firms reinvest in the same time period, and the wage rate is not too high, then the Cournot equilibrium is stable.     

寡头垄断市场三度价格歧视动态博弈分析

对两寡头厂商2元市场用完全信息动态博弈的方法分析了实施三度价格歧视情形和统一定价情形的均衡产量,均衡价格和均衡总收益,并研究了这两种情形三个指标之间的关系.结果显示,在两个子市场的需求函数为线性需求的条件下,统一定价的市场均衡产量等于歧视定价的市场均衡产量;统一定价的均衡价格是歧视定价时两个子市场均衡价格的加权平均;统一定价的市场均衡总收益小于歧视定价的市场均衡总收益.     

Dynamic Model of R&D,Spillovers, and Efficiency of Bertrand and Cournot Equilibria

Using an infinite-horizon two-player differential game, we derive and compare Bertrand and Cournot equilibria for a differentiated duopoly engaging in the process of R&D competition. The main findings of this study are as follows. First, Bertrand competition is more efficient if either R&D productivity is low or products are very different. Second, Cournot competition is more efficient provided that R&D productivity is high, products are close substitutes, and spillovers are not close to zero. This last result is different from what has been obtained in the literature. Hence, this shows that considering a dynamic model and more general investment costs does have an impact on the efficiency results.     

On the Bertrand paradox

In this papel we discuss the classical Bertrand paradox recalling the five known planar probabilistic models and introducing a new continuous family of planar probabilistic models, depending on a parameterx∈]1, +∞[. We also show that two of the classical models can be obtained as the limit, in law, from the new ones, whenx tends to 1 and +∞, respectively.     

On the Bertrand paradox

In this papel we discuss the classical Bertrand paradox recalling the five known planar probabilistic models and introducing a new continuous family of planar probabilistic models, depending on a parameterx∈]1, +∞[. We also show that two of the classical models can be obtained as the limit, in law, from the new ones, whenx tends to 1 and +∞, respectively.     

On the uniqueness of Bertrand equilibrium

We introduce product differentiation in the model of price competition with strictly convex costs in which firms have to supply all of the forthcoming demand. We find that although a continuum of equilibria exists in a homogeneous product market, the competitive price equilibrium is the only robust one. Specifically, as long as the equilibrium correspondence is nonempty, the equilibrium price converges to the competitive price when the degree of product differentiation shrinks to zero.     

Oligopoly newsvendor competition with reference effects

We analyze the equilibrium of a behavioral newsvendor game featuring oligopoly competition, where each newsvendor’s decision is driven by a reference effect regarding her potential profit. We find that the equilibrium order quantities are characterized by behavioral critical fractiles, where each newsvendor only accounts for the actions of competitors with smaller behavioral critical fractiles. Our result generalizes findings from recent literature on duopoly newsvendor competition with reference effects.     

Advertising in a Differential Oligopoly Game

We illustrate a differential oligopoly game where firms compete à la Cournot in homogeneous goods in the market phase and invest in advertising activities aimed at increasing the consumers reservation price. Such investments produce external effects, characterizing the advertising activity as a public good. We derive the open-loop and closed-loop Nash equilibria, and show that the properties of the equilibria depend on the curvature of the market demand function. The comparative assessment of these equilibria shows that the firms advertising efforts are larger in the open-loop equilibrium than in the closed-loop equilibrium. We also show that a cartel involving all the firms, setting both output levels and advertising efforts, may produce a steady state where the social welfare level is higher than the social welfare levels associated with both open-loop and closed-loop noncooperative settings.     

Algorithms for the Network Oligopoly Problem

Network oligopoly models have been recently proposed as an alternative to general equilibrium models for analysing conflict situations between spatially separated firms. However, the oligopoly models are, from an algorithmic standpoint, less well understood than their equilibrium counterparts. In this paper we propose four iterative schemes for computing Cournot-Nash equilibria on congested transportation networks. The algorithms will be analysed theoretically, and computational results will be provided (i) for an oligopoly test problem, and (ii) for a small-scale network oligopoly problem.     

A Differential Oligopoly Game Under Price Competition

Acta Mathematicae Applicatae Sinica, English Series - A dynamic actual demand function was used to portray a market environment for fast moving consumer goods and to establish oligopoly...     

The explicit form of the Bertrand metric

The problem of explicit form of the metric of revolution on Bertrand’s Riemannian manifolds in particular coordinates is solved. Connections with earlier results of M. Santoprete are discussed.     

Resource Dynamics under Partial Cooperation in an Oligopoly

We study the long-run evolution of a renewable resource which is subject to harvest by partially cooperating players who sell the harvested quantities on distinct markets. We derive explicit expressions for the total harvesting quantity of all players in this general framework and investigate the dependence of the total and relative harvest rates on the level of cooperation, available fish stock, and fishing costs. Combining the biological growth model with oligopoly leads to a nonlinear dynamic law for the evolution of the fish stock in the presence of commercial fishing. We provide also existence results for its equilibrium and examine the asymptotic behavior of the equilibrium. We are grateful for the critical comments and suggestions of three anonymous referees.     

Maximum-revenue tariff under Bertrand duopoly with unknown costs

This paper considers an international trade under Bertrand model with differentiated products and with unknown production costs. The home government imposes a specific import tariff per unit of imports from the foreign firm. We prove that this tariff is decreasing in the expected production costs of the foreign firm and increasing in the production costs of the home firm. Furthermore, it is increasing in the degree of product substitutability. We also show that an increase in the tariff results in both firms increasing their prices, an increase in both expected sales and expected profits for the home firm, and a decrease in both expected sales and expected profits for the foreign firm.     

The dynamics of Bertrand model with bounded rationality

The paper considers a Bertrand model with bounded rational. A duopoly game is modelled by two nonlinear difference equations. By using the theory of bifurcations of dynamical systems, the existence and stability for the equilibria of this system are obtained. Numerical simulations used to show bifurcations diagrams, phase portraits for various parameters and sensitive dependence on initial conditions. We observe that an increase of the speed of adjustment of bounded rational player may change the stability of Nash equilibrium point and cause bifurcation and chaos to occur. The analysis and results in this paper are interesting in mathematics and economics.