Cournot, bertrand, and modern game theory

Although it is not generally remembered or known, Cournot applied his equilibrium concept to both quantity rivalry and price rivalry. This makes some of the nomenclature in modern game theory seriously inappropriate. Several critics, past and present, have treated Cournot's quantity rivalry case as only conveniently veiled price rivalry. If Cournot's mathematics are pursued far enough, it is clear that he had a method that symmetrically applies to both quantity rivalry and price rivalry.     

Dimand-Dore on cournot-bertrand: A reply and more

This note refutes the novel thesis of Jean Magnan de Bornier [1992] that all of Cournot's analysis in his 1838 classic was about price rivalry. It also reiterates the proposition that Cournot treated both quantity and price rivalry and that Cournot was clearly aware of the symmetry between quantity conjectures and price conjectures in 1838. It is conjectured that the many misinterpretations of Cournot derive from failure to work through Cournot's simple mathematics and a mental truncation of the Recherches into just Chapter VII.     

Spatial Cournot Competition among Multi-Plant Firms in a Circular City

We characterize equilibrium plant locations for a spatial multi-plant Cournot oligopoly in a circular city. Previous work demonstrates that for a two-plant duopoly, all four plants are equally spaced. We establish that the equilibrium location pattern is unique if there are two firms with an equal number of plants. In most other scenarios, multiple equilibria arise. Next, we endogenously determine both the number of plants per firm and plant locations for a duopoly. It is shown that the subgame perfect Nash equilibrium may not be unique, and for identical set-up costs, the firms may choose different numbers of plants.     

Cournot, Bertrand, and game theory: A further note

This note synthesizes the discussion on the role of Cournot and Bertrand in the analysis of duopoly by drawing on the history of the debate. We conclude that while Bertrand presented a critique of the mathematical economics of Cournot and stimulated the analysis of strategic choice in game theory, he did not present a duopoly model with price as a strategic variable, as opposed to Cournot's model with quantity. In fact, Cournot has both types of models. We show that Irving Fisher contributed to the myth about Bertrand's duopoly theory.     

Mixed oligopoly,endogenous timing and mergers

The present paper discusses endogenous timing in a mixed oligopoly model, comprising one public firm and two private firms, assuming both a merger between the two private firms and between one private and one public firm. The paper proves that although a merger between the two private firms does not change the timing of the game, a merger between the public firm and the private firm into a mixed firm could change the market structure from Stackelberg to Cournot competition.     

产品市场对寡头企业资本结构的影响——考虑破产成本的模型

从战略角度看,寡头企业的资本结构与产品市场密切相关,受到"有限责任效应"和破产成本效应的双重制约。企业对负债水平的选择实际是对这两种相互对立的制约因素的权衡。本文以一个典型的两阶段古诺博弈模型证明了,随着负债水平由低到高,企业的整体价值先升后降;在拐点处,企业实现了"最优资本结构"。     

Strategic trade policy and the home bias in firm ownership structure

In this note we consider the preferences of a profit maximising firm for international ownership in a world in which firms compete in an international Cournot oligopoly, and in which countries use strategic trade policy. We find that firms prefer national ownership and show that full indigenisation occurs in the equilibrium.     

Does a tariff really enhance welfare?

Tanaka (1993) argues the small reciprocal tariff reduces the average costs of firms and enhances the world welfare under a free entry Cournot oligopoly with increasing returns to scale. This paper shows the welfare improving effect which was found in Tanaka (1993) results from the relaxation of the excess entry. We also find, however, such a world welfare enhancing tariff is not valid because of the instability of the Cournot solution. It indicates that we must take great care about the stability in using the Cournot oligopoly model with increasing returns to scale.     

Mergers, welfare, and concentration: Results from a model of stackelberg-cournot oligopoly

This paper explores the relationship between mergers, welfare, and concentration, using a two-stage oligopoly model that generalizes the Cournot and Stackelberg models. This model has been used to show that some profitable mergers raise welfare and that some welfare-lowering mergers are unprofitable. Based on this, one might conclude that policy designed to restrict mergers is unnecessary or even counterproductive. This present paper examines in greater detail the implications of this model and finds that a merger's effects depend not only on the reduction in the number of firms, but also on premerger and postmerger firm behavior. In fact, most mergers lower welfare, and many of these are profitable. Usually, but not always, changes in concentration and welfare are negatively related.     

Industrial Concentration Reverses the Timing in a Trade Policy Game

Faced with an export subsidy by a foreign government, importing countries have to decide whether they should impose countervailing duties or not. Using a Cournot duopoly model, Collie (Weltwirtschaftliches Archiv 130: 191–209) shows that the subgame perfect equilibrium occurs when the importing country sets its production subsidy and tariff at stage one and the foreign government sets its export subsidy at stage two. That is, an importing country will choose to commit itself not to use countervailing duties. In this paper, we extend Collie's duopoly model to the case of a Cournot oligopoly and show that the country in which industry is less concentrated tends to emerge as the Stackelberg leader.     

外商直接投资与市场准入制度变迁

本文在管制俘虏理论、古诺博弈模型等的基础上,以垄断行业的市场准入制度为例,对我国引入FDI的制度变迁意义、FDI促进我国制度变迁的机制等问题,进行了模型化的分析。指出民企并不会由于垄断行业对外企开放而必然获得市场准入机会;并分析了在外企和民企之间的制度双轨制,以及垄断企业、外企参与寻租的数量、投入租金等对民企市场准入制度变迁的影响。     

Corporate Social Responsibility or Payoff Asymmetry? A Study of an Endogenous Timing Game

We revisit an endogenous timing game by introducing corporate social responsibility into firms' payoffs. Previous research investigates an endogenous timing game in a mixed oligopoly, wherein one welfare‐maximizing public firm competes against profit‐maximizing private firms. It shows that the outcome is completely different from that of private oligopoly. In contrast to its result, we find that this change in payoff does not matter as long as the payoffs are symmetric. Our result indicates that asymmetry, and not welfare‐concerning objectives, yields specific results in the literature on mixed oligopoly.     

Regulating the Anticommons: Insights from Public‐Expenditure Theory

This article offers a new interpretation of the traditional Cournot complements problem, or anticommons, by using the theory of public goods to gain a perspective on the problem. Specifically, I examine the pricing strategies and regulation of multiple monopolies that produce products which consumers view as perfect complements. I show that collusion by the firms increases total social welfare and that the collusion problem can be reinterpreted as a problem of provision of public goods from the point of view of the firms. I take this insight further and derive the familiar concepts of the Samuelson marginal condition and the ratio equilibrium for the firms. I compare these outcomes to the first best solution and then apply incentive‐compatible mechanisms to strategically implement the Pareto superior ratio‐equilibrium outcome and the optimal marginal‐cost pricing outcome. Finally, I show how this methodology can be applied to the more familiar Cournot model of oligopoly.     

Quality and Quantity Competition in a Multiproduct Duopoly

This article proposes a Cournot model of two‐stage competition to examine the patterns of vertical product differentiation in a multiproduct duopoly. Firms simultaneously choose the number of products and their qualities at the first stage and compete in quantities at the second stage. We show that when the fixed setup cost of a product is high enough to result in a monopoly outcome, the monopolist always sells a single product. Moreover, in any equilibrium of a multiproduct duopoly, quality differentiation between them will develop into a nonsegmented pattern because each firm desires to avoid a strong effect of cannibalization. The set of equilibria reveals the properties of quality differentiation between multiproduct firms. In a multiproduct duopoly, the profit from a high‐quality product can be lower than that from a low‐quality product. This finding sharply contrasts with the literature on single‐product firms, which finds the high‐quality advantage.     

Market structure, pigouvian taxation, and welfare

Using a short-run partial equilibrium model of social welfare, this paper examines the social welfare implications of changing Pigouvian taxes under three markets: perfect competition, monopoly, and Cournot oligopoly. The result for perfect competition supports the earlier finding that Pigouvian taxation increases social welfare [Buchanan, 1969]. However, in contrast to the previous result that Pigouvian taxes lower welfare under monopoly, the authors show that if the noncompetitive distortion is small, these taxes might still be useful in correcting monopoly-generated externalities and in improving social welfare. Cournot firms react to the tax depending upon their individual perceptions of the gain in post-tax marginal revenue. Policy implications of the study's results are discussed.     

Mr. Gripsrud and a theory of oligopoly

Conclusions May I sum up my reply to Mr. Gripsrud by noting: (1) I do not believe his critique of my position on differential payments for uncertainty is properly founded. But I readily recognize that a reading of only a single paper and/or even isolated parts of a book could easily cause the concern he had in this regard. I rather imagine, in fact, that had I been him, I too might have had the same concern. (2) As for his critique of my cost curve, here again I can only suggest my belief that what I set forth is appropriate. At the best, I would refer him to the original text for a more complete answer; at the least, the suggestions given above in this reply will hopefully resolve the matter under discussion. (3) As for his objection to my average revenue schedule, I can only propose that in theory we sometimes utilize conceptions which abstract sharply from the true world around us. But this does not make the theory wrong! (4) Possibly his most important critique really goes beyond the paper in question and was answered in the book. I would suggest, accordingly, that he misread my thesis that an unorganized (competitive) oligopoly market is isomorphic to the purely competitive market. What he is suggesting as helpful tools for analysis would be those that I could accept for short-run matters without loss of position. In other words, nothing in my theory of the spatial firm precludes his quest for new paradigms to shed light on selected problems uppermost in his mind.     

战略性出口关税:能够有效缓解贸易摩擦的短期措施

本文运用异质产品的古诺(伯川德)模型以及将水平、垂直差异化产品纳入D-S模型,分析了战略性出口关税对于出口行业,进口竞争行业以及进口国社会福利的影响,并将结果与其他战略性贸易政策进行对比和分析。我们的结论是:我国通过战略性出口关税来缓解贸易摩擦的效果要优于使用其他战略性贸易政策,这有利于调整出口产业结构,培育出口企业自身能力,并与我国的长期发展目标相吻合。但是战略性出口关税可能带来的社会经济问题不容忽视。     

R&D Collaboration Networks in Mixed Oligopoly

We develop a model of endogenous network formation in order to examine the incentives for R&D collaboration in a mixed oligopoly. Our analysis reveals that the complete network, where each firm collaborates with all others, is uniquely stable. When R&D subsidies are not available, in addition to the complete network, the private partial and the private‐hub star networks are Pareto efficient. However, the complete network becomes the unique Pareto efficient network when R&D is subsidized. This result is in contrast with earlier contributions in private oligopoly where under strong market rivalry a conflict between stable and efficient networks is likely to occur. It also highlights the role of a public firm as policy instrument in aligning individual incentives for collaboration with the objective of efficiency, independently of whether R&D subsidies are provided by the regulator.     

Strategic corporate social responsibility of high-speed rail in China

This paper investigates the strategic corporate social responsibility (CSR) of a high-speed rail (HSR) firm when competing with an airline firm in a differentiated transportation market and the interactions with government environmental policies in the context of a Cournot–Bertrand comparison. We find that a standard CSR chosen by the government is lower under Cournot than that under Bertrand when both the marginal cost of HSR and product substitutability are low enough, while a voluntary CSR chosen by the HSR operator is always higher under Cournot than that under Bertrand. We also find that the voluntary CSR could be higher or lower than the standard CSR, depending on marginal costs, product substitutability, and competition modes. We then show that when the government imposes an environmental tax together with CSR activities, both the strategic CSR and environmental tax are always lower under Cournot than those under Bertrand. Finally, we show that equilibrium traffic volumes, ticket fares, consumer welfare, and social welfare are independent of competition modes with environmental tax.     

Firm specific human capital and unemployment in a growing economy

This study analyzes how the intensive use of firm specific human capital in firms affects the unemployment rate. For this purpose, I introduce into an equilibrium search model the possibility that workers quit their jobs. A worker changes his job when a firm that newly enters into the market offers a higher wage than his current wage. If firm specific human capital is important, it is difficult for a worker to quit his job, and, in consequence, the number of workers who quit their jobs is small. Thus, the unemployment rate is low. If the speed of technology obsolescence is high, the unemployment rate is high.