Mixed oligopoly with consistent conjectures

In this paper, we consider a model of mixed oligopoly with conjectural variations equilibrium (CVE). The agents’ conjectures concern the price variations depending upon their production output’s increase or decrease. We establish existence and uniqueness results for the conjectural variations equilibrium (called an exterior equilibrium) for any set of feasible conjectures. To introduce the notion of an interior equilibrium, we develop a consistency criterion for the conjectures (referred to as influence coefficients) and prove the existence theorem for the interior equilibrium (understood as a CVE with consistent conjectures). To prepare the base for the extension of our results to the case of non-differentiable demand functions, we also investigate the behavior of the consistent conjectures in dependence upon a parameter representing the demand function’s derivative with respect to the market price.     

基于产量理性推测导数的差异产品企业研发决策

文章通过将推测导数引入企业研发的AJ模型，考察差异产品企业在理性或一致性推测的条件下研发策略和研发投入的变化，通过企业产品差异化参数将寡头企业研发决策扩展到产品相关的企业之间，从而扩大了AJ模型均衡的一般性，文章还给出一致性推测条件下的两种不同类别产品企业研发投入最优成本缩减反应曲线斜率和均衡成本缩减量与溢出效应之间的关系。     

Numerical experimentation with a human migration model

In this paper, we develop a human migration model with a conjectural variations equilibrium (CVE). In contrast to previous works we extend the model to the case where the conjectural variations coefficients may be not only constants, but also (continuously differentiable) functions of the total population at the destination and of the group’s fraction in it. Moreover, we allow these functions to take distinct values at the abandoned location and at the destination. As an experimental verification of the proposed model, we develop a specific form of the model based upon relevant population data of a three-city agglomeration at the boundary of two Mexican states: Durango (Dgo.) and Coahuila (Coah.). Namely, we consider the 1980–2000 dynamics of population growth in the three cities: Torreón (Coah.), Gómez Palacio (Dgo.) and Lerdo (Dgo.), and propose utility functions of four various kinds for each of the three cities. After having collected necessary information about the average movement and transportation (i.e., migration) costs for each pair of the cities, we apply the above-mentioned human migration model to this example. Numerical experiments have been conducted with interesting results concerning the probable equilibrium states revealed.     

基于推测弹性的双寡头研发AJ模型最优成本缩减决策

文章通过将推测弹性引入AJ模型,首先考察一致性推测弹性对双寡头企业研发策略的影响,从而得出有推测的双寡头市场结构下的研发均衡结果,然后将零一致性推测弹性的均衡成本缩减量与AJ模型的结果进行对比,最后给出一致性推测弹性和溢出系数之间的关系对研发绩效的影响效果.     

Open versus closed loop capacity equilibria in electricity markets under perfect and oligopolistic competition

We consider two game-theoretic models of the generation capacity expansion problem in liberalized electricity markets. The first is an open loop equilibrium model, where generation companies simultaneously choose capacities and quantities to maximize their individual profit. The second is a closed loop model, in which companies first choose capacities maximizing their profit anticipating the market equilibrium outcomes in the second stage. The latter problem is an equilibrium problem with equilibrium constraints. In both models, the intensity of competition among producers in the energy market is frequently represented using conjectural variations. Considering one load period, we show that for any choice of conjectural variations ranging from perfect competition to Cournot, the closed loop equilibrium coincides with the Cournot open loop equilibrium, thereby obtaining a ‘Kreps and Scheinkman’-like result and extending it to arbitrary strategic behavior. When expanding the model framework to multiple load periods, the closed loop equilibria for different conjectural variations can diverge from each other and from open loop equilibria. We also present and analyze alternative conjectured price response models with switching conjectures. Surprisingly, the rank ordering of the closed loop equilibria in terms of consumer surplus and market efficiency (as measured by total social welfare) is ambiguous. Thus, regulatory approaches that force marginal cost-based bidding in spot markets may diminish market efficiency and consumer welfare by dampening incentives for investment. We also show that the closed loop capacity yielded by a conjectured price response second stage competition can be less or equal to the closed loop Cournot capacity, and that the former capacity cannot exceed the latter when there are symmetric agents and two load periods.     

Service quality,outsourcing and upward channel decentralization

We build a model to analyse the benefit of upward channel decentralization for a firm choosing service outsourcing and integration. The key findings of this paper are as follows. First, we formulate an upward channel decentralization problem as a game incorporating consumer behaviour of willingness to pay in a channel duopoly. Our model considers (i) service quality, (ii) consumer marginal willingness to pay (MWTP), and (iii) consumer perceivable difference. A supply chain firm’s preference of outsourcing strategy depends on the monotonicity of both the failure rate (or Mills Ratio) and CDF-PDF ratio of MWTP distribution function. Second, we use this model to explore the benefit of retailer strategy of upward channel decentralization. An equilibrium can be achieved by benefiting the low-label product with low quality service but deteriorating the high-label channel product with high quality.     

Dynamic Advertising Under Vertical Product Differentiation

We investigate a dynamic advertising model where product quality is endogenous. In the differential game between single-product firms, there exists a parameter range where the low-quality firm uses a more efficient advertising technology and earns higher profits than the rival. Moreover, we show that equilibrium qualities are the same under duopoly, multiproduct monopoly, and social planning, the only distortion being concerned with the output levels.     

Estimating conjectural variations for electricity market models

Agents’ behavior in oligopolistic markets has traditionally been represented by equilibrium models. Recently, several approaches based on conjectural variations equilibrium models have been proposed for representing agents’ behavior in electrical power markets. These models provide insight of market equilibrium sensitivity to agents’ strategies and external variables, and therefore, they are widely applied. Unfortunately, not enough analysis has been done in how these user-supplied parameters, the conjectural variations, should be estimated. This paper proposes a parameter inference procedure based on two stages. The first stage infers historical values of the parameter by fitting the models’ results to historical market data. The second stage is based on a statistical time-series model whose objective is to forecast parameter values in future scenarios. Additionally, results of this procedure’s application to a real-size case are presented.     

Endogenous timing in a mixed duopoly

This paper applies the framework of endogenous timing in games to mixed quantity duopoly, wherein a private—domestic or foreign—firm competes with a public, welfare-maximizing firm. A central goal of the paper is to present a unified and general treatment of the basic question of what constitutes the appropriate solution concept—Cournot or Stackelberg—in such duopolies. We show that simultaneous play never emerges as a subgame-perfect equilibrium of the extended game, in sharp contrast to private duopoly games. We demonstrate that this result is due to the objective function of the public firm being increasing in the rival’s output (instead of decreasing for a private firm). We provide sufficient conditions for the emergence of public and/or private leadership equilibrium. In all cases, private profits and social welfare are higher than under the corresponding Cournot equilibrium. We make extensive use of the basic results from the theory of supermodular games in order to avoid common extraneous assumptions such as concavity, existence and uniqueness of the different equilibria, whenever possible. Some policy implications are drawn, in particular those relating to the merits of privatization.     

Competitive Price Equilibrium with Consumer Reservation Utility

This paper studies a competitive price equilibrium in the market of a product category where consumers are homogeneous with a reservation utility below which they will not purchase the product. The impact of the reservation utility on the price equilibrium is of particular interest, because the reservation utility may change according to the business cycle and economic environments. Using multinomial logit model to describe market response, we study the comparative statics of the prices, profits and market shares of firms, each of which produces one brand in the product category, with respect to the reservation utility in the Nash equilibrium. It is shown that, as the reservation utility increases, the prices as well as the profits at Nash equilibrium decrease. Also, in the case of duopoly market, the firm with lower cost structure will increase its market share as the reservation utility increases.     

Strategic optimization in R&D investment

We use d'Aspremont and Jacquemin's strategic optimal R&D investment in a duopoly Cournot competition model to construct myopic optimal discrete and continuous R&D dynamics. We show that for some high initial production costs, the success or failure of a firm is very sensitive to small variations in its initial R&D investment strategies.     

基于吸收能力的企业合作研发的动态模型

竞争还是合作,是企业研发投资时所面临的选择,本文应用最优控制论建立了一个考虑吸收能力的企业合作研发的动态模型,分析了双寡头垄断企业在竞争和合作两种情况下的均衡研发投资,并与D＇aspremont ＆ J＇aquemin的静态模型的结果进行了比较.     

Consistent conjectures are optimal Cournot-Nash strategies in the meta-game

In this paper, we investigate the properties of consistent conjectural variations equilibrium developed for a single-commodity oligopoly. Although, in general, the consistent conjectures are distinct from those of Cournot-Nash, we establish the following remarkable fact. Define a meta-game as such where the players are the same agents as in the original oligopoly but now using the conjectures as their strategies. Then the consistent conjectures of the original oligopoly game provide for the Cournot-Nash optimal strategies in the meta-game.     

New product introduction and capacity investment by incumbents: Effects of size on strategy

We analyze a duopoly where capacity-constrained firms offer an established product and have the option to offer an additional new and differentiated product. We show that the firm with the smaller capacity on the established market has a higher incentive to innovate and reaches a larger market share on the market for the new product. An increase in capacity of the larger firm can prevent its competitor from innovating, whereas an increase in capacity of the smaller firm cannot prevent innovation of its larger competitor. In equilibrium the firm with smaller capacity on the established market might outperform the larger firm with respect to total payoffs.     

A note on the equilibria of an economic model with local competition “à la Cournot”

Guirao and Rubio (2010) [12] introduce an economic model, which generalizes the classical duopoly of Cournot type, where the competitors are located around a circle or a line and each firm competes “à la Cournot” with its right and left neighboring. For the case of having three and four players, we describe completely the bifurcations of equilibria in terms of the production costs of each firm and we study the stability of them. Moreover, for the case of four players we provide some information on the two-periodic orbits of the system.     

Organizational strategy and tacit collusion in oligopoly with agency

We study a model that integrates organizational structure and agency withdynamic price competition in oligopoly. Workers in different levels of the organizational structure have asymmetric information and heterogeneous objectives; i.e., there are agency conflicts within the firm. The organizational strategy of the firm is to determinesequentially the decision power relating to price and non-price competition instruments at each level. We examine the equilibrium organizational and competitive strategy of firms in a duopoly, and characterize the extent of noncooperative tacit collusion (with respect to price and non-price competition) that is feasible. We identify two sets of sufficient conditions that guarantee, (i) the monopoly solution is sustainable at any discount factor (rate of impatience of the workers), or (ii) the monopoly solution is not sustainable for any level of the discount factor. Interestingly, tacit collusion may be feasible when either the agency problem is non-existentor very severe; i.e., firm profits in equilibrium may be non-monotone in the extent of the agency conflict. Our analysis indicates that intrafirm learning and agency will have a stronger impact on feasible tacit collusion in markets where non-price competition plays a strong role. Moreover, there is an intimate connection between the firm's organizational strategy and the extent of tacit collusion with the (industry) business cycle.     

Licensing endogenous cost-reduction in a differentiated Stackelberg model

In this paper we consider a differentiated Stackelberg model, when the leader firm engages in an R&D process that gives an endogenous cost-reducing innovation. The aim is to study the licensing of the cost-reduction by a two-part tariff. By using comparative static analysis, we conclude that the degree of the differentiation of the goods plays an important role in the results. We also do a direct comparison between our model and Cournot duopoly model.     

Asymmetric dynamic price competition with uncertainty

We consider a dynamic setting-price duopoly model in which a dominant (leader) firm moves first and a subordinate (follower) firm moves second. We suppose that each firm has two different technologies, and uses one of them according to a certain probability distribution. The use of either one or the other technology affects the unitary production cost. We analyse the effect of the production costs uncertainty on the profits of the firms, for different values of the intercept demand parameters. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

带有网络外部性的动态寡头垄断定价

给出了带有网络外部性的两阶段寡头垄断定价模型,并用博弈论方法求解.通过与带有网络外部性的完全垄断定价模型的比较,得出重要结论:在网络外部性足够大的情况下,①寡头竞争情况下与完全垄断下情况一样,“科斯假设”将得到克服,均衡定价将呈现先低后高的情况.②对于完全垄断厂商来说,网络外部性k的增加能够增加其利润,但对于寡头竞争的企业来说,正好相反,k的增加将导致其利润的下降.