Individual best response in the repeated Cournot model

We propose a particular style of punishments to support collusive behavior in an infinitely repeated Cournot oligopoly model for at least the same range of discount factors as Friedman’s trigger strategies. The punishment lasts for a finite number of periods and asymmetry is introduced in such a way that each punisher’s output is the individual best response.      

A new look for Stackelberg-Cournot equilibria in oligopolistic markets

Summary. This note deals with Cournot type oligopolies in which the market clearing price occasionally may be non-unique. A Stackelberg leading producer is present. Given that setting we explore continuity properties of the followers' reaction and provide sufficient conditions for existence of equilibrium. Received: June 20, 2000; revised version: April 24, 2001     

Information Advantage in Cournot Oligopoly

Consider an oligopolistic industry where firms have access to the same technology but are asymmetrically informed about the environment. Even though it is commonplace to think that in this context superior information leads to higher profits, we find that under Cournot competition this is not generally the case: It holds when firms' technology exhibits constant returns to scale, but it does not necessarily hold otherwise. Journal of Economic Literature Classification Numbers: C72, D43, L13.     

Profit sharing and strike activity in Cournot oligopoly

Within an incomplete-information framework, we develop a model of wage determination in a unionized Cournot oligopoly. The assumption of incomplete information allows the possibility of strikes or lockouts, which waste industry potential resources, at equilibrium. Facing such deadweight loss, the government or the social planner may decide to adopt a policy, such as a profit-sharing scheme. Under two different bargaining structures (firm level vs. industry level), we investigate the effects of adopting profit sharing on the wage outcome and the strike activity. If the base-wage bargaining takes place at the industry level, then the introduction of a profit-sharing scheme increases the strike activity. But if the base-wage bargaining takes place at the firm level and the number of firms in the industry is greater than two, then the introduction of a profit-sharing scheme reduces the strike activity.     

Strategic managerial incentives in a two-period Cournot duopoly

This paper examines the nature of optimal managerial incentives in the context of a duopoly marked by competition between the firm's managers in a dynamic production environment. If the marginal cost of production falls moderately over time or remains unchanged, there exists an equilibrium where one owner requires her manager to maximize profit, whereas the rival-owner requires her manager to maximize sales revenue. The profit-maximizing manager turns his firm into a Stackelberg-leader, while the sales-revenue-maximizing manager turns his firm into a Stackelberg-follower. Further, the profit-maximizing manager may generate a larger firm profit relative to the sales-revenue-maximizing manager.     

基于同时博弈和序贯博弈的寡头市场古诺均衡比较分析

根据国内外在古诺模型研究上的缺陷,分别从古诺假定、产品差异、成本差异以及非线性市场需求等方面对垄断市场结构中厂商之间同时博弈与序贯博弈两种情况的均衡状况进行比较分析,得出寡头垄断市场中厂商之间的均衡与产品质量、成本状况、市场需求以及博弈的顺序等因素有关的结论,从而为中国相关行业的决策提供理论依据。     

A dynamic Stackelberg model with production-adjustment costs

We investigate the (dynamic) stability of a stackelberg oligopoly model of a market of a homogeneous good, with output competition, one Stackelberg leader and a number of identical followers. We assume that each firm incurs quadratic production-adjustment costs if it changes its output. We present a simple necessary and sufficient condition for stability of the model. Using the condition, we compare the stability of this model with the stability of two related Cournot models in which all firms present are followers. It turns out that the Stackelberg model is more stable than these two Cournot models.     

Cournot games with biconcave demand

Biconcavity is a simple condition on inverse demand that corresponds to the ordinary concept of concavity after simultaneous parameterized transformations of price and quantity. The notion is employed here in the framework of the homogeneous-good Cournot model with potentially heterogeneous firms. The analysis leads to unified conditions, respectively, for the existence of a pure-strategy equilibrium via nonincreasing best-response selections, for existence via quasiconcavity, and for the uniqueness of the equilibrium. The usefulness of the generalizations is illustrated in cases where inverse demand is either “nearly linear” or isoelastic. It is also shown that commonly made assumptions regarding large outputs are often redundant.     

Teaching Cournot Without Derivatives

The author presents a simple technique for teaching the Cournot model to first-year students. The approach involves demonstrating to the students that out of all rectangles with a common perimeter, the square has the greatest area. No use is made of derivatives. The same approach can be used to understand some other market forms.     

Non-renewable resource Stackelberg games

The market structure for many mineral industries can be described as oligopoly with potential for Stackelberg leadership. This paper derives and analyzes dynamically consistent extraction equilibria in a two-period discrete-time “Truly” Stackelberg (TS) model of non-renewable resource extraction, where firms move sequentially within each period and where both the leader and follower have market power. We show how the leader may be able to manipulate extraction patterns by exploiting resource constraints. Whether the leader wants to speed up its own production relative to the Cournot–Nash (CN) equilibrium depends on the shape of its iso-profit curve, which is affected by the two firms’ relative stock endowments and relative production costs. If the leader extracts faster, then the follower extracts slower, but in aggregate the industry extracts faster. Unlike static Stackelberg games, the follower does not necessarily have a second mover disadvantage.     

不对称R＆D活动下的市场绩效分析——基于有差异产品的寡头市场

为了研究在Stackelberg寡头竞争模型下企业在产品市场是否合作对市场绩效的影响,建立了寡头市场中面向R＆D工艺的两阶段博弈模型。采用逆向归纳法求出了产品市场合作与不合作两种情况下的古诺-均衡解。研究表明,从促进技术进步的角度来看,对于R＆D效率不太高的R＆D项目,产品市场合作策略优于产品市场竞争策略。从提高企业利润的角度来看,对于R＆D效率较高的R＆D项目,当产品差异不大时,产品市场合作策略优于产品市场竞争策略;当产品差异较大时,产品市场竞争策略优于产品市场合作策略。对于R＆D效率较低的R＆D项目,产品市场竞争策略优于产品市场合作策略。从提高消费者剩余以及改善社会福利的角度来看,对于R＆D效率较低的R＆D项目,产品市场竞争策略优于产品市场合作策略。     

A Cournot Mechanism for Pollution Control under Asymmetric Information

The contribution of this paper is to show that a simple nonlinear tax can achieve a long-run socially optimal level of pollution without the regulator knowing marginal abatement costs. Firms are charged their differential contribution to total damages, evaluated at the upper margin of current emissions. This induces a Cournot game in pollution levels. We show that the Nash equilibrium exists, corresponds to the socially optimal long-run output and emission levels and number of firms, is stable, and can be reached by iterative computations where conjectures are formed using a linear estimator based on past emission levels.     

Pareto-Efficient Solutions for Shared Public Good Provision: Nash Bargaining versus Exchange-Matching-Lindahl

We compare two cooperation mechanisms for consumer/producers of a public good: the Nash Bargaining Solution (NBS) and the Exchange-Matching-Lindahl (EML) solution, where each agent specifies her demand for and supply of the public good according to her personal exchange rate. Both mechanisms are Pareto-efficient. EML is equivalent to matching. In our specific model with linear or quadratic benefits and quadratic costs, EML and NBS are equivalent when there are two agents. With more than two agents, the high-benefit/low-cost agents are better off under EML. We also analyze outsourcing, where agent i can pay agent j to produce the amount that agent i promised to contribute. In our specific model, payments from high-cost to low-cost agents (and from high-benefit to low-benefit agents) are (usually) lower in EML than in NBS.     

On the convergence to the Nash bargaining solution for action-dependent bargaining protocols

We consider a non-cooperative multilateral bargaining game and study an action-dependent bargaining protocol, that is, the probability with which a player becomes the proposer in a round of bargaining depends on the identity of the player who previously rejected. An important example is the frequently studied rejector-becomes-proposer protocol. We focus on subgame perfect equilibria in stationary strategies which are shown to exist and to be efficient. Equilibrium proposals do not depend on the probability to propose conditional on the rejection by another player. We consider the limit, as the bargaining friction vanishes. In case no player has a positive probability to propose conditional on his rejection, each player receives his utopia payoff conditional on being recognized. Otherwise, equilibrium proposals of all players converge to a weighted Nash bargaining solution, where the weights are determined by the probability to propose conditional on one's own rejection.     

FEE VERSUS ROYALTY POLICY IN LICENSING THROUGH BARGAINING: AN APPLICATION OF THE NASH BARGAINING SOLUTION

In this paper, we consider a Cournot duopoly market in which the patent‐holding firm negotiates with its rival firm about payments for licensing a cost‐reducing innovation. Applying the Nash bargaining solution, we compare two licensing policies, a fixed fee and a royalty. Our results are as follows. Royalty licensing is better than fixed fee licensing for both firms if the innovation is not drastic. So, royalty licensing is always carried out. Moreover, though there exists a case in which consumers prefer fixed fee licensing, royalty licensing is always superior to fixed fee licensing from the social point of view.     

Bertrand versus Cournot competition in a downstream mixed oligopoly with foreign ownership

Focusing on foreign ownership in the private firm, we examine the Cournot-Bertrand comparison in a mixed oligopolistic market with vertical market structure. We have found that if public and private firms were charged with uniform price for their inputs, then Cournot-Bertrand ranking in market outcomes confirms those obtained by Ghosh and Mitra (2010). This implies that under uniform pricing in the upstream sector, the vertical market structure does not have substantial influences on Cournot-Bertrand ranking. However, if discriminatory pricing is adopted, firm's profits, output, and social welfare are often reversed to those obtained from uniform pricing in the upstream sector. Given the closeness of products, if the share of foreign ownership is sufficiently low, social welfare in Cournot competition can exceed that of Bertrand competition, contrasting with the standard welfare ranking that Bertrand welfare is strictly higher than Cournot. This implies that Cournot competition can be more socially desirable than Bertrand in mixed oligopoly with vertical market structure if discriminatory pricing scheme is adopted by foreign upstream monopolists.     

A Theory of Mergers and Merger Waves

We consider a sequential merger game between Cournot firms with homogeneous product and quadratic cost. A large slope of the marginal cost function or a small slope of inverse market demand are both predicted to increase the incentive to merge. The profitability of any merger increases with the number of mergers having already taken place. Thus, mergers tend to occur in waves in industries that have experienced exogenous shocks affecting firms’ cost or demand. We also show some mergers that are not profitable for merged firms in the short-run may take place in the early stage of a wave.     

Wage bargaining and employment revisited: separability and efficiency in collective bargaining*

We analyse the two-dimensional Nash bargaining solution (NBS) by deploying the standard labour market negotiations model of McDonald and Solow. We show that the two-dimensional bargaining problem can be decomposed into two one-dimensional problems, such that the two solutions together replicate the solution of the two-dimensional problem if the NBS is applied. The axiom of “independence of irrelevant alternatives” is shown to be crucial for this type of decomposability. This result has significant implications for actual negotiations because it allows for the decomposition of a multi-dimensional bargaining problem into one-dimensional problems – and thus helps to facilitate real-world negotiations.     

基于古诺模型的电力市场排污收费制度研究

本文运用经济学原理及古诺博弈模型对电力市场的排污收费制度进行研究，分析排污收费前后电力市场均衡的变化，推导出了古诺博弈均衡的通用解，分析了企业排污系数（βi）、企业边际生产成本（bi）和政府施行的排污收费税率（r）对均衡结果的影响，分析了征收排污费过程中发电企业的行为选择过程，认为电力企业从自身利益出发，会根据排污收费税率（r）来调整其排污量。最后提出了政府如何制定排污税率的建议。