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.     

双寡头竞争下最优进口贸易政策选择

文章在水平差别产品的伯川德模型中对从量和从价关税进行了分析比较。研究发现,效用函数必须满足一些严格的假设,才能保证征收关税将改善本国社会福利。从量关税的进口限制效果明显强于从价关税。但对于均衡从量关税,总存在一个对能给本国带来更高社会福利的从价关税。两者的差距取决于均衡点本国市场对外国产品的需求弹性,需求弹性越小,社会福利差距越大。     

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.     

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.     

地方政府对国外直接投资税率竞争的博弈分析

本文采用伯川德价格竞争模型研究两个地方政府如何制定税率来竞争一个外商投资项目。分析了企业在不同地区投资的价值由公有信息和私有信息组成时,投资环境的异同对于均衡税率的影响。若投资环境同质,两地方政府税率竞争均衡时税率为零;若投资环境对企业有差异,均衡税率大于零。两种情况下的均衡税率都低于社会福利最大化时的税率水平。     

Endogenous Price Leadership and the Strategic Acquisition of Information

We model a differentiated Bertrand duopoly in which a firm's earlier knowledge of market demand than its competitor results in endogenous price leadership with the information advantaged firm leading. In such a setting with second‐mover advantage, we then study the firms’ incentives to acquire information and analyze an information acquisition game. Both (i) neither firm acquiring information and (ii) one firm acquiring information can arise as subgame perfect equilibrium, but both firms acquiring information is never an equilibrium outcome, even if information is free. Information may have a negative value if it causes a change in the timing of price competition.     

Testing Oil Refiners' Conduct in Korea: A Differentiated Product Approach

This paper investigates oil refiners' conduct in the Korean gasoline market. Specifically, I examine which of two modes of conduct, Bertrand–Nash competition or collusion, better fits the data. Unlike previous literature, this paper employs a differentiated product approach to address the stylized discrepancy in refiners' brands' prices: stable stratification of prices among refiners, but an unlikely equilibrium outcome in the homogenous goods market. Correct understanding of refiners' conduct is important because appropriate policy responses to collusion differ significantly from appropriate responses to competition‐driven outcomes. The results of this paper support the hypothesis that Bertrand–Nash competition better explains refiners' conduct.     

Cournot–Bertrand comparisons under R&D competition: Output versus R&D subsidies

We compare Cournot and Bertrand competitions with R&D investment under output versus R&D subsidy policies. We demonstrate that Cournot firms invest more (less) in R&D and the government grants more (less) subsidies than for Bertrand firms with output (R&D) subsidies. We also find that both competition modes yield the same welfare with output subsidy, while Bertrand yields higher welfare than Cournot with R&D subsidy. Finally, firms' profits and welfare in Cournot are higher under output subsidies, while they can be higher in Bertrand under R&D subsidies if the product substitutability is high and the firm's R&D investment is efficient.     

Tacit Collusion in Price‐Setting Duopoly Markets: Experimental Evidence with Complements and Substitutes

We study the effect of demand structure on the ability of subjects to tacitly collude on prices by considering Bertrand substitutes and Bertrand complements. We find evidence of collusion in the complements treatment, but no such evidence is found in the substitutes treatment. This finding is somewhat in contrast with a previous study that observes tacit collusion in two treatments with similar underlying demand structures but with no market framing.     

Forecasting Inflation: An Art as Well as a Science!

Summary In this study, we build two forecasting models to predict inflation Harmonised Index of Consumer Prices (HICP) for the Netherlands and for the euro area. The models provide point forecasts and prediction intervals for both the components of the HICP and the aggregated HICP -index itself. Both models are small-scale linear time series models allowing for long-run equilibrium relationships between HICP components and other variables, notably the hourly wage rate and the import or producer prices. The model for the Netherlands is used to generate the Dutch inflation projections for the eurosystem’s Narrow Inflation Projection Exercise (NIPE). The recursive forecast errors for several forecast horizons are evaluated for all models, and are found to outperform a naive forecast and optimal AR models. Moreover, the same result holds for the Dutch NIPE projections, which have been provided quarterly since 1999. The aggregation method to predict total HICP inflation generally outperforms the direct method, except for long horizons in the case of the Netherlands. We thank an anonymous referee of this journal and participants of the second Conference of the Euro Area Business Cycle Network, the 10th International Conference on Computing in Economics and Finance and seminar participants at De Nederlandsche Bank, Erasmus University Rotterdam and Maastricht University, in particular Filippo Altissimo, Bob Chirinko, Bertrand Candelon, Denise Osborn and Adrian Pagan for useful comments.     

Variety,Globalization, and Social Efficiency

The standard formal presentation of the Dixit‐Stiglitz‐Krugman (DSK) model of monopolistic competition with a constant‐elasticity‐of‐substitution (CES) utility function supposes a sufficient number of firms so that the elasticity of demand facing each variety is approximated by a constant elasticity of substitution. Such a formulation forces economies of scale to be frozen so that firm size never changes. We use a Bertrand‐Nash interpretation of the equilibrium that allows the elasticity of demand facing each variety to depend on the number of varieties, thus allowing the gains from globalization to reflect both the increase in variety and the exploitation of economies of scale. We also develop a precise expression for per capita real income with any number of sectors and examine the age‐old question of the socially optimal number of varieties.     

Endogenous price leadership in a duopoly: Equal products, unequal technology

In the present paper we study endogenous price leadership in the context of a homogeneous product Bertrand duopoly model in which the firms have different, strictly convex cost functions. In such a framework it is well known that a simultaneous move price choice game does not have an equilibrium in pure strategies, but it has an equilibrium in mixed strategies. In the Stackelberg games with an exogenous price leader, we show that a pure strategy subgame perfect Nash equilibrium (SPNE) always exists. Although the SPNE might not be unique, the payoffs are the same across all SPNE. Finally, we analyze the issue of endogenous price leadership using the continuous version of the Robson (1990) timing game. The result is unexpected. One would expect the more efficient firm to emerge as the endogenous price leader. This is not always true. In most cases the endogenous leader is the firm with the highest "threshold" price. However, we also provide conditions under which the more efficient firm emerges as the leader. Our paper essentially complements Yano (2001) , which is based on the Hamilton and Slutsky (1990) framework.     

Sticky prices as a coordination success

Recent contributions have articulated ways in which price rigidities signal breakdowns of coordination. These contributions are aimed at unifying New Keynesian economics by linking the issue of nominal price flexibility with that of between-firm coordination. By contrast, this paper demonstrates that sticky prices can signal a coordination success rather than a coordination failure. A model is developed in which N firms face a stochastic industry demand and engage in (infinitely) repeated Bertrand competition. In each period, firms are able to learn the realization of the demand shock but at a positive cost. The existence of two equilibria—one featuring sticky prices and the other featuring flexible prices—is proved. These equilibria are then compared. The equilibrium featuring sticky prices Pareto-dominates that featuring the flexible ones.     

Effect of a tariff on the environment and welfare: The case of an environmental differentiated duopoly in a Green Market

Employing a model of environmental quality-differentiated products, we analyze the effect of an ad valorem tariff on the unit emission level of the products, the environment and welfare in the Bertrand and the Cournot duopoly cases, respectively. We show that the effect of the tariff policy depends on the mode of market competition and the degree of marginal social valuation of environmental damage.     

Incorporating fairness in generalized games of matching pennies

We examine individual behavior in generalized games of matching pennies. We have three main findings. First, individuals cooperate in these games; that is, they systematically select strategies that lead both players to obtain higher expected payoffs than in a Nash equilibrium. Second, existing models that assume altruistic preferences do not explain the cooperative behavior in these games. Third, among the main models in the extant literature, the only one that predicts the observed behavior is the quantal response equilibrium.     

外生单向溢出效应下纵向差异化产品Cournot和Bertrand竞争均衡的比较研究

研究价格(Bertrand)和数量(Cournot)竞争模式下,单向溢出对企业质量选择、利润的影响。以纵向差异化市场结构为例,建立了基于单向质量溢出的不对称寡头竞争模型,运用赋值计算对模型的均衡解进行了比较分析,结论是:1给定溢出因子和学习效应的合理取值范围,领先和跟随企业的质量与利润在价格竞争下都小于数量竞争;2质量间的单向溢出效应、跟随者的学习努力都会导致领先者初始质量的下降,但在价格竞争时,这种"逆向选择"效应的程度较低;3跟随者的学习激励随着溢出效应的提高而降低,并不受竞争策略变化的影响。这些发现可以解释中国轿车产业竞争模式对合资和自主创新企业关系变化的影响。     

Supermodularity and Complementarity in Economics: An Elementary Survey

The literature on supermodular optimization and games is surveyed from the perspective of potential users in economics. This methodology provides a new approach for comparative statics based only on critical assumptions, and allows a general analysis of games with strategic complementarities. The results are presented in a simplified yet rigourous manner, without reference to lattice theory, for the special case of one-dimensional parameter and actions sets, with the emphasis being on wide accessibility. Detailed applications are presented for well-known models of consumer behavior, monopoly pass-through, Bertrand and Cournot competition, strategic R&D, search, and matching. Wherever appropriate, useful tricks for applications and comparative comments are inserted.     

Strategic R&D policy in a quality-differentiated industry with three exporting countries

We examine strategic research and development (R&D) policy for quality-differentiated products in a third-market trade model. We extend the previous work by adding a third exporting country, so that the market structure is international triopoly. We show that the presence of the third exporting country affects strategic R&D policies. With three exporting countries, the lowest-quality exporting country gains from taxing domestic R&D and the middle-quality exporting country gains from subsidizing domestic R&D under both Bertrand and Cournot competition. As in the duopoly case, however, the optimal unilateral policy for the highest-quality exporting country depends on the mode of competition. Various cases of policy coordination by exporting countries are also examined.     

The Logit Equilibrium: A Perspective on Intuitive Behavioral Anomalies

This paper considers a class of models in which rank-based payoffs are sensitive to “noise” in decision making. Examples include auctions, price competition, coordination, and location games. Observed laboratory behavior in these games is often responsive to the asymmetric costs associated with deviations from the Nash equilibrium. These payoff-asymmetry effects are incorporated in an approach that introduces noisy behavior via a logit probabilistic choice function. In the resulting logit equilibrium, behavior is characterized by a probability distribution that satisfies a “rational expectations” consistency condition: The beliefs that determine players' expected payoffs match the decision distributions that arise from applying the logit rule to those expected payoffs. We prove existence of a unique, symmetric logit equilibrium and derive comparative statics results. The paper provides a unified perspective on many recent laboratory studies of games in which Nash equilibrium predictions are inconsistent with both intuition and experimental evidence.