Unionized Bertrand Duopoly and Strategic Export Policy

The paper reports that an export subsidy is optimal for a unionized Bertrand duopoly. Following results published by Brander and Spencer ( Journal of International Economics , 1988, pp. 217–34), this establishes the robustness of export subsidization to the mode of competition (Cournot or Bertrand), and contrasts with nonunion results in the literature. If both firms are unionized and both governments pursue active trade policies, a subsidy remains optimal except for a narrow range of extreme substitutability between products. Nations with a lower opportunity cost of labor employ more aggressive policies in equilibrium.     

A Two-stage Price-setting Duopoly: Bertrand or Stackelberg

This paper investigates a two-stage price-setting duopoly with differentiated goods. First, each firm announces its price; second, it chooses its actual price; and finally the market opens. Once a firm announces a price, it is able to discount it but not raise it. The model includes Stackelberg-type and Bertrand-type equilibria as possible outcomes. Whether Bertrand or Stackelberg appears in equilibrium depends on the properties of demand functions crucially. We find three patterns of equilibrium outcomes; one case has Bertrand equilibrium only, another has Stackelberg only, and the other has both equilibria     

A Note on Optimal Industrial Policy Towards Bertrand Homogeneous Duopoly

Recent studies in strategic trade and industrial policy analysis suggest that an investment subsidy, in the form of an R&D subsidy, a capacity subsidy or an advertising subsidy, would be a robust industrial policy recommendation towards an international differentiated oligopoly. However, in this paper, we show that this result does not carry over to the case of a Bertrand homogeneous duopoly. This result together with the fact that the optimal industrial policy is to set an investment subsidy when in product market competition firms play a Cournot output game, imply immediately that there hardly exists a robust industrial policy recommendation towards homogeneous goods industries.     

On the Cournot–Bertrand Profit Differential and the Structure of Unionisation in a Managerial Duopoly

This paper deals with the issue of the Cournot–Bertrand profit differential by bringing together two different strands of the industrial organisation literature: managerial delegation and unionised oligopolies. Relative to unionisation, two alternative regimes are analysed and compared: ‘decentralised unionisation’, involving firm‐specific unions, and ‘centralised unionisation’, in which an industry‐wide union sets a uniform wage for the entire industry. The ‘reversal result’ – that is, profits are higher under Bertrand than under Cournot – applies irrespective of the unionisation regime and for a very wide range of product differentiation. Moreover, it is more likely to occur when unionisation is decentralised than centralised and, especially when products are not too much differentiated, the profit differential in favour of price competition is also larger in the presence of firm‐specific unions. However, if firm owners not only delegate the choice of the strategic variable but also that of the competition regime, managers always opt to compete in quantities, thus generating an inefficient choice for owners.     

Leapfrogging in switching systems

The rapid emergence of new technologies has increased the rate of obsolescene. This creates the possibility that developing countries and, in particular, newly industrializing countries may leapfrog older generations of technologies. We lay out the issues and variables to the considered for an understanding of leapfrogging in telephone switching systems. In particular, we distinguish between demand-driven and infrastructure-driven leapfrogging. Data for the early 1980s offer some evidence that demand-driven leapfrogging was most prevalent in countries with intermediate network maturity. Infrastructure-driven leapfrogging has taken place mainly in France, South Korea, Taiwan, and Singapore.     

全球化与技术跨越

全球化带来技术经济范式的转换，技术经济范式的转换使发展中国家在追赶发达国家过程中陷入困境，由此提出技术跨越是赶超之利器。     

Coalition-proof Bertrand equilibria

Summary. This paper examines the coalition-proof Nash equilibria of a Bertrand model of price competition where firms supply all demand. When firms are asymmetric we prove existence and provide a sufficient condition for uniqueness. For symmetric firms, we show that an equilibrium is necessarily unique. We also examine whether this unique equilibrium outcome is implementable through a sequential move game where the firms take turns at announcing prices. Finally we examine the limiting property of such equilibria as the number of firms go to infinity.Received: 20 March 2002, Revised: 5 August 2003JEL Classification Numbers: D43, D41, L13.Correspondence to: Kunal SenguptaWe are deeply indebted to an anonymous referee for very helpful and incisive comments that led to substantial improvements in the paper. We also gratefully acknowledge the hospitality of the Department of Finance, Hong Kong University of Science and Technology where much of the work on this paper was carried out.     

Duopoly signal jamming

Summary This paper examines a repeated duopoly market with heterogeneous outputs. Firms have (common) prior beliefs over the values of an unknown parameter of each firm's demand curve. Firms cannot observe rivals' quantities, but can observe market prices, which are subject to random disturbances and hence provide noisy information that firms use to update their beliefs concerning the unknown parameters' values. Each firm can potentially signal jam, or strategically vary its output level in order to manipulate the distribution of likely market prices and hence the likely inferences drawn by the opponent. We find that the opportunity to signal-jam introduces two conflicting effects, arising out of the desire to manipulate expectations concerning each of the two demand curves. Depending upon the relative magnitudes of these two effects, signal-jamming may lead firms to either increase or decrease period-one quantities. If the firms are symmetric, then the opportunity to signal jam induces both firms to increase output in order to induce their rival to conclude that demand is unfavorable. However, if the firms believe almost surely that one of the possible parameter values is true for firm 2's demand curve (for example), then firm 1 may signal-jam by producing less output.We thank two anonymous referees, an associate editor and Pieter Kop Jansen for helpful comments that corrected some errors. Larry Samuelson is grateful to the Center for Economic Research at Tilburg University and the Department of Economics at the University of Bonn for support. Financial support by the Deutsche Forschungsgemeinschaft (DFG) through Sonderforschungsbereich 303 is gratefully acknowledged.     

兼并和伯特兰德竞争的价格效应分析

本文采用博弈论方法研究兼并和伯特兰德竞争对价格、竞争等的影响.首先,分布在两个市场中的寡头公司分别选择同市场或跨市场的兼并活动,其次,两个市场中的寡头公司进行伯特兰德竞争.结论显示,有关需求函数的各种约束条件是决定价格升高或下降的关键因素,从而揭示了价格效应产生的原理.美国航空业的案例研究支持模型的基本结论.     

Market Instability in a Stackelberg Duopoly

m -period duopoly model with inventory costs, where each firm chooses when to produce. We find that, in contrast to most existing works concerning endogenous roles of the firms, no pure strategy equilibrium exists when m is strictly larger than two. This result indicates that no stable pattern of allocation of roles exists except for a two-period model; thus the leader-follower relationship inevitably becomes instable. Received August 1, 2000; revised version received July 20, 2001     

Mixed Duopoly and Environment

We show under general demand and cost conditions that in a mixed duopoly with pollution the government can implement the socially optimal outputs and abatements by a tax‐subsidy scheme and keeping the public firm fully public. The scheme requires taxing outputs and subsidizing abatements at different rates, unlike a pollution tax. Our result improves on the shortcoming of a pollution tax to implement the social optimum. We also show that when the private firm is partly foreign‐owned, the government will adopt some privatization and will not implement the social optimum, though the social optimum is implementable.     

Cournot and Bertrand Games

The author describes a series of matrix choice games illustrating monopoly, shared monopoly, Cournot, Bertrand, and Stackelberg behavior given either perfect complements or perfect substitutes. The games are created by using a spreadsheet to fill out a profit table given the choices of two players. One player selects the column, the other the row, and the table gives the profit of the row chooser. Because each player has a table, each thinks of him- or herself as the row chooser and the other as the column chooser. The games may be applied to international trade through the traditional Boeing v. Airbus story or, more currently, through foreign sales corporations. Addition of Bertrand competition allows discussion of price wars, and addition of perfect complements allows discussion of the proposed Microsoft breakup.     

Tax competition in a Bertrand model

We show that in Bertrand models pure-strategy equilibria exist only under extraordinarily restrictive assumptions. We analyze tax competition between two countries for foreign investment. In the symmetric case of equal gross profits of the firms, zero-taxation is the unique equilibrium in pure strategies. If gross profits differ between countries only -equilibria can exist. However, if the tax rate applies to foreign investment as well as to domestic sources no equilibria exist in pure strategies. The same holds true if countries compete for firms that differ in gross profit opportunities, unless extremely unrealistic conditions are met.     

Limit-pricing as Bertrand equilibrium

Summary. We consider a Bertrand duopoly model with increasing returns to scale where one of the firms have a cost advantage and prices vary over a grid. We find that typically more than one equilibria exist. However, there are only two perfect equilibria. Moreover, as the size of the grid becomes small, both these equilibria converge to the limit-pricing outcome. Received: February 25, 2000; revised version: January 9, 2001     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

不同角度的"技术跨越"

技术跨越是技术后进国家赶超技术先进国家的重要途径，那么，究竟什么是技术跨越？从不同角度界定的“技术跨越”有着不同的内涵。     

Bowley Duopoly Under Vertical Relations

Compared to the well‐known oligopoly models such as those of Cournot, the so‐called Bowley duopoly is less known, and almost ignored in the literature. This neglect reflects the assumption that as a leader–leader model incorporating apparent excess rivalry it is presumably untenable, at least in theory. However, it is, in fact, observable in practice. Furthermore, the predicted excess competition is not only observable empirically but also accountable theoretically. We show how excess competition emerges when an upstream monopolist offers the downstream retailers a compensated game in which each acts as a leader. The outcome is not only stable but also benefits all involved actors, including consumers under vertically‐related markets, such as those presided over by a monopolist producer. This result of emergent stability shows that the Bowley duopoly should be considered alongside other oligopoly models.     

Bertrand Games and Sharing Rules

We consider asymmetric Bertrand games with arbitrary payoffs at ties or sharing rules, and identify sufficient conditions for the zero-profit outcome and the existence of Nash equilibria. Subject to some technical conditions on non-tied payoffs the following hold. If the sharing rule is strictly tie-decreasing all players but one receive zero equilibrium payoffs, while everybody does so if non-tied payoffs are symmetric. Mixed (pure) strategy Nash equilibria exist if the sharing rule is (norm) tie-decreasing and coalition-monotone. I would like to thank Fernando Branco, the audience at Pompeu Fabra (Barcelona), ISEG (Lisbon), University of Mannheim, ESEM 2003 (Venice), EARIE 2005 (Porto), two anonymous referees, and the editor Dan Kovenock for very useful comments. This research received financial support under project POCTI/ECO/37925/2001 of FCT and FEDER.