The impact of the number of sellers on quantal response equilibrium predictions in Bertrand oligopolies

This paper studies how increasing the number of sellers in a Bertrand oligopoly with homogenous goods affects the equilibrium price level predicted by logistic quantal response equilibrium (LQRE) and power‐function QRE (PQRE). We show that increasing the number of sellers reduces the average posted price in a PQRE, but can increase the average posted price in an LQRE. Our results indicate that the comparative‐static predictions of QRE (McKelvey & Palfrey, 1995, Games Econ Behav, 10, 6–38) are not necessarily robust to changes of the quantal response function.     

Bertrand Price Undercutting: A Brief Classroom Demonstration

The author presents a brief classroom demonstration illustrating Bertrand price undercutting. The demonstration is appropriate for micro principles and intermediate- and upper-level undergraduate classes, as well as graduate classes in micro, industrial organization, and game theory.     

Managerial firms’ profitability,unions, and environmental taxes

This article examines how determining an optimal environmental tax in a Cournot duopoly with unionized labour markets and managerial firms departing from the strict profit-maximization. It is shown that firm-specific monopoly unions that set wages (1) reduce both the environmental tax and environmental damage and (2) counterintuitively, increase firms’ profitability when the abatement technology is not too “efficient”, and the public evaluation of environmental quality is sufficiently high. Within this framework, the work also develops the endogenous game played by firms that must choose between sales delegation (SD) and profit-maximization. Results show that the SD contract always emerges as the unique, deadlock sub-game perfect Nash equilibrium, thereby solving the (prisoner's) dilemma emerging in the related existing literature assuming a competitive labour market.     

Licensing cost-reducing innovations under supply function competition

In this paper, we study the licensing of cost-reducing innovations in a duopoly under supply function competition. We show that the innovator prefers fixed-fee licensing to no licensing if its cost advantage is not extremely large. Moreover, if its cost advantage is not extremely small, the innovator prefers fixed-fee licensing and mixed licensing to revenue-royalty licensing. This second result arises only because of our assumption that the cost functions are quadratic. We show that if the cost functions are linear and royalty payments are per unit of output, the innovator strictly prefers royalty licensing to fixed-fee licensing. We also show that in our model, consumer surplus is remarkably higher under any type of licensing than under no licensing. However, revenue-royalty licensing is slightly superior for consumers to the other two types of licensing and only so if the cost advantage of the innovator is sufficiently large.     

Optimal Investment Decisions for Two Positioned Firms Competing in a Duopoly Market with Hidden Competitors

This paper extends the literature dealing with the option to invest in a duopoly market for a leader‐follower setting. A restrictive assumption embodied in the models in the current literature is that investment opportunities are semi‐proprietary in that the two identified or positioned firms are guaranteed to hold at least the follower's position. More competition is realistically captured in our model by introducing the concept of hidden rivals so that the places in the market can be taken not only by positioned firm but also by these hidden competitors. The value functions and the optimal triggers for the positioned firms differ materially in settings with(out) the presence of hidden rivals. Unlike existing models, our model allows for (a)symmetric market shares and investment costs for the leader and the follower. Cooperative entrance by the two positioned firms is also modelled.     

Existence of Bertrand equilibrium revisited

In this paper we reconsider existence of Bertrand equilibrium in a symmetric‐cost, homogenous‐product oligopoly. We prove the following main results. (a) If the cost function is strictly superadditive on [0, ∞) then there exists a pure strategy Bertrand equilibrium. Such Bertrand equilibria are necessarily non‐unique. (b) If the cost function is strictly subadditive on [0, ∞) then there exists no Bertrand equilibrium, either in pure strategies or in mixed strategies.     

基于不同保护目的的最优关税分析

从不同的保护目的出发,可将最优关税区分为最佳福利关税和最大收入关税。假定一个国家自身生产一种产品,同时进口另外一种产品,且两种产品的质量不同,分析最佳福利关税和最大收入关税问题,结果发现：第一,如果本国的产品质量较低而进口的产品质量较高,那么,无论企业之间是进行Bertrand竞争还是Cournot竞争,假如国外企业的效率较高（低）,那么最大收入关税大（小）于最佳福利关税;此外,Cournot竞争条件下的最佳福利关税和最大收入关税分别高于Bertrand竞争条件下的最佳福利关税和最大收入关税。第二,如果本国的产品质量较高而进口的产品质量较低,那么当本国企业的效率较低（高）时,最大收入关税高（低）于最佳福利关税。     

一个具有双寡头垄断性质的三边贸易模型——以石油市场为例的国家福利实验模拟分析

中国作为大宗商品的国际大买家,争取国际定价权已经成为再也无法回避的问题.有鉴于此出,文章以石油为例,着重探讨石油定价战略选择的经济学机理,在一个具有双寡头垄断性质的三边贸易体系中,对OPEC和非OPEC石油输出国之间的博弈进行了一般均衡分析.根据模型设定参数及实验模拟发现,在Cournot双寡头垄断下,国家M的福利水平增加32.4%,而国家F的福利水平却下降0.8%.由此作出的解释是:与M相反,F是石油净进口国家,高油价和商品y较低的相对价格所产生的负面效应要大于闲暇带来的正面效应.此时,整个社会福利下降0.7%.石油在消费者效用函数中的权重较小时,石油生产的一个负向冲击对福利损失的影响非常有限.在F和M的纯策略集合{双寡头垄断,完全竞争,不生产石油}中,存在唯一的纳什均衡{完全竞争,完全竞争},这使得国家H和F从中获益.模型给人的启示是,除了尽快完善国家石油战略储备体系外,中国应积极参与到石油定价权的争夺中,改变目前完全被动承受油价变动影响的不利地位.     

Market Power,Industrial Organization and Tradeable Quotas

Individual Transferable Quotas (ITQs) wereintroduced into the Mid-Atlantic Surf Clam and OceanQuahog fishery to reduce over-capitalization whileconserving clam populations. Because the number ofoperators in the fishery declined drastically sincethe introduction of this policy, there is concernabout its effect on competitiveness. This paperutilizes Bertrand Pricing Models to show thatmonopoly power is absent from the surf clam andocean quahog markets. Concentration ratios, Lorenzcurves and Gini Coefficients estimated for thefishery for periods before and after ITQintroduction support the results of the Bertrand model.     

The value of commitment in Stackelberg games with observation costs

We study Stackelberg games in which the follower faces a cost for observing the leader's action. We show that, irrespective of the size of the cost, the leader's value of commitment is lost completely in all pure-strategy equilibria. However, there also exists a mixed-strategy equilibrium that fully preserves the first-mover advantage. In this type of equilibrium, the probability that the follower looks at the leader's action is independent of the cost of looking.