Cournot Duopoly With Multi-period Competition: Inventory as a Coordination Device

This paper analyses a Cournot duopoly model with finitely repeated competition. Each firm is allowed to hold inventories for a period. When there are more than two periods, inventory-holdings encourage firms to take collusive actions. By holding large inventories, a firm can commit to large sales in the next period, giving inventories a strategic value. When a firm deviates from collusion, the strategic value of inventories allows the non-defecting firm to become the Stackelberg leader in future markets, forcing the defecting firm to become the Stackelberg follower. Collusive sales can be attained with this threat of punishment.     

A Mixed Duopoly With Switching Costs

We examine the effects of switching costs in a two‐period Hotelling‐type model where a profit‐maximising private firm competes with a welfare‐maximising public firm. We show that, in contrast with the case in which both firms are private, where switching costs raise prices in both periods, in the mixed duopoly they raise prices in the second period but reduce them in the first period. Moreover, the first‐period price reduction is of such magnitude that switching costs reduce firms’ profits and raise consumer welfare. We also find that switching costs affect the consequences of privatisation in favour of firms and against consumers.     

Delegation and Information Sharing in Cournot Duopoly

Information sharing in oligopoly has been analyzed by assuming that firms behave as a sole economic agent. In this paper it is assumed that ownership and management are separated. Contrary to the classical result of information sharing in a Cournot duopoly with private cost information, the paper shows that information sharing is no longer always a dominant strategy and expected consumer surplus is no longer always decreased. The paper determines the circumstances under which information is exchanged and analyzes its welfare consequences.      

A Two-stage Price-setting Duopoly: Bertrand or Stackelberg

This paper investigates a two-stage price-setting duopoly with differentiated goods. First, each firm announces its price; second, it chooses its actual price; and finally the market opens. Once a firm announces a price, it is able to discount it but not raise it. The model includes Stackelberg-type and Bertrand-type equilibria as possible outcomes. Whether Bertrand or Stackelberg appears in equilibrium depends on the properties of demand functions crucially. We find three patterns of equilibrium outcomes; one case has Bertrand equilibrium only, another has Stackelberg only, and the other has both equilibria     

转移成本、价格歧视和非对称寡头竞争

通过在Hotelling空间差异模型的基础上结合转移成本构建非对称企业竞争博弈模型.主要研究在非对称情况下,两企业在一致定价与价格歧视下竞争的均衡结果.还对两种不同定价体制下的均衡结果进行了比较,分析价格歧视是否强化竞争.研究发现价格歧视对竞争的效应是不确定的,很大程度受到两企业不对称程度的影响.     

The Dynamics of Duopoly Output Games Involving Cournot and Related Best-Response Strategies*

The paper considers a variety of perfect information duopoly games involving the Cournot and related best-response strategies. Firms record their output at the end of each business period. At the beginning of a new period they have to plan their new output; they do so in an attempt to maximize their profits. The importance of discrete time and the resulting time interval between successive outputs is discussed. The difference equations appropriate to the various games are solved exactly, and it is shown that there is always a stable approach to equilibrium at the Cournot point. The convergence of the solutions is discussed.     

A cake for Cournot

A cake division mechanism is presented that is equivalent in terms of the size of the pieces of the cake n players’ receive in equilibrium to the quantities that n firms in a Cournot oligopoly supply in equilibrium. This mechanism extends to equivalence between cake division and Nash’s ‘divide the dollar’ game.     

加工贸易框架下进出口对汇率变动的响应特征——基于古诺双寡头模型的探讨

通过构建一个包含跨国加工模式和本土生产模式的双寡头模型可以分析“加工贸易”框架下汇率变动对进出口的影响.模型推导发现加工国货币相对消费终端国货币贬值,则加工国对消费终端国加工商品的出口值将上升,从消费终端国进口同类商品值(中间品)也将上升,且出口对汇率变动的反应滞后于进口对汇率变动的反应.商品的汇率弹性与商品的自身属性相关,较大的出口汇率弹性对应较大的进口弹性.加工贸易框架下,虽然加工商品出口的汇率弹性要小于同类商品(中间品)进口的汇率弹性,但如果进口值相对出口值的比率较小,则加工国本币贬值依然改善其国际收支状况.文中以中国和意大利纺织品贸易类别细分的数据对上述模型推导的结论进行了实证检验.     

A Model of a Price-setting Duopoly with a Wage-rise Contract

This paper considers a wage-rise contract between a firm and its employees as the firm's strategy, and suggests a wage-rise-contract policy. The policy is a promise by the firm that it will announce a certain output level and a wage premium rate, and if it actually produces more than the announced output level, then it will pay each employee a wage premium uniformly. First, this paper examines the case in which one of two firms unilaterally offers the wage-rise-contract policy by using a two-stage price-setting duopoly model. It is then shown that there exists an equilibrium which coincides with the Stackelberg solution where the firm adopting the policy is the leader. Next, this paper examines the case in which both firms can offer the wage-rise-contract policy in the model. It is then shown that there exists an equilibrium which is more profitable for both firms than in the unilateral case.     

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.     

A Note on Auction Quotas with a Foreign Duopoly*

A country importing a good from foreign duopolists may improve its welfare by imposing a quota on the good at the free trade quantity and giving a fraction of the quota licences to the duopolists while auctioning off the rest.     

Exploring Duopoly Markets with Conjectural Variations

In this article, the authors investigate competitive firm behaviors in a two-firm environment assuming linear cost and demand functions. By introducing conjectural variations, they capture the different market structures as specific configurations of a more general model. Conjectural variations are based on the assumption that each firm believes its own strategy influences its rival's strategy. Firms derive their optimal choice from these exogenous conjectures, under the form of a conjectural best-response function. The authors’ approach fully encompasses the standard measures of market power (the Lerner Index) and concentration (the Herfindahl Index), both depending on the conjectural variations. They finally represent, analytically and graphically, the equilibrium strategies and the associated indexes in a unified framework for any level of competition, ranging from perfect competition to collusion.     

Duopoly competitions with capacity constrained input

This paper focuses on the duopoly substitutability product with an upstream input subjected to capacity constraints. The effects of capacity constraints are captured. Combining competition effect with constraint effect, some interesting conclusions are reached. First, the relationship between capacity constraints and firm size is addressed. We argue that the capacity constraints reduce market size difference and price difference under Cournot. Second, under the Stackelberg case, the existence of solution is proved, and Stackelberg competitions enlarge firm-size difference and price difference if the more efficient firm plays the leading position. When the weaker firm plays the leading position, the conclusions depend on the total capacity. Finally, under the Stackelberg case, when the stronger firm plays the leading position, the firm-size difference and price difference decrease with total input under capacity constraints, which is contrary to the conclusions under Cournot competitions.     

Cournot duopoly with two production periods

We modify the Cournot model by allowing for two production periods before the market clears. The firms choose outputs simultaneously in the first period. These outputs become common knowledge and then the firms choose how much more to produce in the second period before the market clears. Any outcome on the outer envelope of the best-response functions between and including the firms' smallest Stackelberg outcomes is sustainable as a subgame perfect Nash equilibrium.     

Labor-managed Cournot oligopoly with product differentiation

Two dynamic systems of labor adjustments are formulated for labor-managed firms in Cournot oligopoly with product differentiation. The global stability conditions are derived for two types of Cournot equilibria corresponding to the stationary points of the two dynamic systems.The author is grateful to two referees of this Journal for helpful comments, which have led to a radical revision of an earlier version.     

Duopoly Competition with Corporate Social Responsibility

This paper highlights the effect of firms’ position on firms’ strategies with corporate social responsibility (CSR) practices under three different cases: Cournot competition; Stackelberg competition with the CSR firm taking the leader position and turnover, with the profit maximising (PM) firm playing as the leader. Some interesting conclusions are achieved. First, the CSR firm always produces more than the PM firm. Second, the outputs of both firms (the consumer surplus) under the PM firm's leading position are larger than those under Cournot. Third, the profits of both firms (producer surplus) under the PM firm playing the leading position are less than those under Cournot. Surprisingly, when the PM firm first moves, the PM firm's profits are the lowest while the CSR firm's outputs are the highest in all three cases. Finally, the relationship of social welfare under the three cases is ambiguous.     

Duopoly models with a joint capacity constraint

The paper proposes a two-stage mixed duopoly model of exhaustible resource market where at the first stage the government decides on the degree of privatization of public firm and at the second stage the public and private firms decide simultaneously on the two-period extraction paths. It is demonstrated that if the two firms have symmetric technologies with increasing marginal extraction costs and the same resource stocks, then neither full nationalization of any of the two firms nor full privatization will be socially desirable. It is shown that the presence of a semi-public firm improves intertemporal allocation of the fixed resource stock. Thus, partial privatization is optimal even under exogenously fixed total outputs of each firm. For asymmetric cost case, when the public firm is less efficient than the private firm, we derive the conditions under which full nationalization or full privatization is optimal.     

Stackelberg Mixed Duopoly with a Foreign Competitor

We investigate Stackelberg mixed duopoly models where a state‐owned public firm and a foreign private firm compete. We examine a desirable role (either leader or follower) of the public firm. We also consider endogenous roles by adopting the observable delay game of Hamilton and Slutsky (1990). We find that, in contrast to Pal (1998) discussing a case of domestic competitors, the public firm should be the leader and that it becomes the leader in the endogenous role game. We also find that in contrast to Ono (1990) eliminating a foreign firm does not improve domestic welfare in mixed oligopolies.