Coalition-proof supply function equilibria in oligopoly

In an industry where firms compete via supply functions, the set of equilibrium outcomes is large. If decreasing supply functions are ruled out, this set is reduced significantly, but remains large. Specifically, the set of prices that can be sustained by supply function equilibria is the interval between the competitive price and the Cournot price. In sharp contrast, when the number of firms is above a threshold we identify (e.g., three if demand is linear), only the Cournot outcome can be sustained by a coalition-proof supply function equilibrium.     

Optimal cartel trigger price strategies

A dynamical model of industry equilibrium is described in which a cartel deters deviations from collusive output levels by threatening to produce at Cournot quantities for a period of fixed duration whenever the market price falls below some trigger price. In this model firms can observe only their own production level and a common market price. The market demand curve is assumed to have a stochastic component, so that an unexpectedly low price may signal either deviations from collusive output levels or a “downward” demand shock.     

ENDOGENOUS TIMING AND STRATEGIC CHOICE: THE COURNOT‐BERTRAND MODEL

Cournot establishes a Nash equilibrium to a duopoly game under output competition; Bertrand finds a different Nash equilibrium under price competition. Both treat the strategic choice variable (output versus price) and the timing of play as exogenous. We investigate Cournot‐Bertrand models where one firm competes in output and the other competes in price in both static and dynamic settings. We also develop a general model where both the timing of play and the strategic choice variables are endogenous. Consistent with the conduct of Honda and Scion, we show that Cournot‐Bertrand behaviour can be a Nash equilibrium outcome.     

THE OUTPUT EFFECT UNDER OLIGOPOLISTIC THIRD DEGREE PRICE DISCRIMINATION*

This paper analyses the output effect of price discrimination in a Cournot oligopoly where firms have different costs. Criteria which are based on the demand curves but not on the industry cost structure are developed to determine the direction of output change. Such criteria may provide an analytical basis for assessing regulatory cases and developing empirical propositions in testing the social impact of oligopolistic price discrimination.     

Competition with Congestible Networks

We analyse competition between two network providers when the quality of each network depends negatively on the number of customers connected to that network. With respect to price competition we provide a sufficient condition for the existence of a unique pure strategy Nash equilibrium. Comparative statics show that as the congestion effect gets stronger quantities will decrease and prices increase, under both Bertrand and Cournot competition. In an example with endogenous capacities it turns out that equilibrium capacities are at first increasing and then decreasing in the strength of congestion. Furthermore, capacities are higher under Cournot competition. Welfare comparisons between Bertrand and Cournot competition are unambiguous for fixed capacities, but may turn around for endogenous capacities.     

Distribution effects and the business demand for money

This paper examines whether and how changes in an industry's firm-size distribution affect the per-firm demand for money. The size distribution of an industry potentially affects the demand for money through several channels. We examine four of those channels: 1) economies of scale; 2) decentralization in cash management; 3) cost of credit; and 4) compensating balances. We conclude that increasing the size inequality increases the industry's per-firm demand for money.     

Innovation,licensing, and price vs. quantity competition

In this paper, we develop a differentiated duopoly model with endogenous cost-reducing R&D and review the argument on welfare effect of price and quantity competition in the presence of technology licensing. We show that, with licensing, the standard conclusion on duopoly (Singh and Vives, 1984) is completely reversed. Cournot competition induces lower R&D investment than Bertrand competition does. Moreover, Cournot competition leads to lower prices, lower industry profit, higher consumer surplus and higher social welfare than Bertrand competition.     

On the comparison of price and quantity competition under endogenous timing

This paper compares Bertrand and Cournot equilibria in a differentiated duopoly with linear demand, and asymmetric constant marginal cost under endogenous timing. It shows that endogenous timing leads to two sequential play with both leader–follower configurations in Bertrand, but simultaneous play in Cournot. Moreover, every firm’s mark-up/output ratio and the two firms’ weighted ‘average’ price are all lower, but the two firms’ weighted ‘average’ output is higher in either of the two sequential Bertrand equilibria than in the simultaneous-move Cournot equilibrium.     

BERTRAND Vs. COURNOT COMPETITION WITH UPSTREAM FIRM INVESTMENT

This paper compares Bertrand and Cournot competition in a vertical structure in which the upstream firm sets the input price and makes R&D investments. We show that from the downstream firms’ point of view, Cournot competition has the advantage of a more monopolistic effect, leading to the setting of a higher price, but has the disadvantage of inducing a lower incentive for the upstream firm to invest. On the other hand, Bertrand competition has the advantage of providing a greater incentive for the upstream firm to invest but has the disadvantage of a more competitive effect, leading to the setting of a lower price. Our main findings are as follows. First, R&D investment level is greater under Bertrand competition than under Cournot competition. Second, from the standpoint of the upstream firm and industry, Bertrand competition is more efficient than Cournot competition. Third, from the standpoint of the downstream firms, Bertrand competition is more efficient than Cournot when investment is sufficiently efficient and products are sufficiently differentiated.     

Contributions to Cournot oligopoly theory

This work contributes to a number of questions concerning oligopoly models. In particular, uniqueness of the Cournot equilibrium point is demonstrated under the assumption that either the unit price function is differentiable and the derivative is strictly negative or the cost functions are strictly convex. Also, under the assumption of either strictly decreasing unit price function or strictly convex cost functions, it is shown that (a) the total production level at equilibrium increases with entry of additional players, (b) that cooperation between some of the players necessarily entails profit for the others, and (c) cooperative grouping causes decrease in production levels.     

The dynamics of some duopoly games involving the Market Share and Nichol strategies

The paper analyses the dynamics of some duopoly output games involving the Cournot, Market-Share and Nichol strategies. The model assumes linear price and cost functions and supposes that outputs are adjusted instantaneously at discrete time intervals. For all games considered, equilibrium is either reached after a finite number of moves or a stable approach to equilibrium occurs as t → ∞. In fact, apart from a few uninteresting cases, arising from the oversimplified form of the Market-Share strategy, all equilibrium points lie on specified parts of the firms' Cournot loci.     

Comparing Cournot and Bertrand equilibria in an asymmetric duopoly with product R&D

We compare the Cournot and Bertrand equilibria in an asymmetric duopoly with product R&D competition. If a firm’s marginal cost is lower than that of its rival, then this firm (its rival) is referred to as the more (less) efficient firm. Under each mode of competition, there are three types of equilibria: blockaded-entry, deterred-entry, and accommodated-entry. Moreover, the presence of R&D investment makes it harder for the less efficient firm to survive. Cournot competition entails a unique equilibrium, whereas Bertrand competition may yield two equilibria. It is harder for the less efficient firm to survive under Bertrand competition than under Cournot competition. Versus Cournot competition, Bertrand competition yields higher industry output, and it shifts production from the less efficient firm to the more efficient firm. This result, together with the known size effect, explains the following three findings. First, the more efficient firm has a normal output ranking, whereas the less efficient firm may demonstrate an output reversal. Second, the more efficient firm may demonstrate a R&D reversal, whereas the less efficient firm has a normal R&D ranking (its Cournot R&D effort exceeds its Bertrand R&D effort). Third, Bertrand competition is more welfare-efficient than Cournot competition.     

Estimating productivity and returns to scale in the US textile industry

In light of the textile industry's growing foreign competition, trade deficit and job loss, we estimate its productivity and efficiency for the period 1975–93 utilizing a variable elasticity of substitution production function. The results indicate that, despite job losses, the industry adjusted by increasing labor productivity and maintaining fairly stable profits. This performance does not warrant protectionist policies. However, with an elasticity of factor substitution less than one and decreasing, the impact of factor price increases could result in higher apparel prices and preference for cheaper imports. Furthermore, with an elasticity of capital output rapidly decreasing, significant technological improvements will be required to improve competitiveness since textile production is capital intensive. Recently revised rules on trade liberalization could increase competition in the industry. First version received: October 1999/Final version received: August 2000     

Bilateral oligopoly and quantity competition

Bilateral oligopoly is a market game with two commodities, allowing strategic behavior on both sides of the market. When the number of buyers is large, bilateral oligopoly approximates a game of quantity competition played by sellers. We present examples which show that this is not typically a Cournot game. Rather, we introduce an alternative game of quantity competition (the market share game) and, appealing to results in the literature on contests, show that this yields the same equilibria as the many-buyer limit of bilateral oligopoly, under standard assumptions on costs and preferences. We also show that the market share and Cournot games have the same equilibria if and only if the price elasticity of the latter is one and investigate the differences in equilibria otherwise. These results lead to necessary and sufficient conditions for the Cournot game to be a good approximation to bilateral oligopoly with many buyers and to an ordering of total output when they are not satisfied.     

WHOLESALE PRICES AND COURNOT‐BERTRAND COMPETITION

This note considers the competing vertical structures framework with Cournot‐Bertrand competition downstream. It shows that the equilibrium wholesale price paid by a Cournot (Bertrand)‐type retailer is above (below) marginal costs of a corresponding manufacturer. This result contrasts with the one under pure competition downstream (i.e., Cournot or Bertrand), where the wholesale price is set below (above) marginal costs in case of a Cournot (Bertrand) game at the retail level.     

Cournot and Stackelberg Duopolies Revisited

First, conditions are derived for a leader (or a follower) to be more advantageous than a follower (or a leader) in Stackelberg duopoly with symmetric firms and without product differentiation. Second, the equilibria in Cournot and Stackelberg duopolies are compared under a set of reasonable assumptions. If the reaction function slopes upward, the Cournot duopolists' profits turn out to be lower than those of both the Stackelberg leader and follower, and the equilibrium industry output is smaller in Stackelberg duopoly than in Cournot duopoly.
JEL Classification Numbers: D21, D43, L13.     

Technological Upgrading under Tariffs and Equivalent Quotas*

This paper compares the effect of tariffs and that of equivalent quotas on the domestic firm’s production technology choice when it competes with a foreign firm in the domestic market. It is shown that under Bertrand price competition, the ranking of technology under tariff protection and quota protection is ambiguous, as it depends on the relative strength of the strategic vs output effects. The equivalent quota regime can generate a higher‐technology (implying a lower production cost) choice than the tariff regime if the strategic effect dominates the output effect. In contrast, the technology level is necessarily higher under the tariff regime than under the equivalent quota regime when the firms engage in Cournot quantity competition.     

International asymmetric R&;D rivalry and industrial strategy

Profit-sharing licensing is quite a common business practice. In a Cournot duopoly model, we showed that if not subject to any restrictions this kind of technology for equity deal would lead to a decline in industry output and hurt consumers. To avoid the industry output contraction and protect the interests of consumers, the government can intervene in licensing by requiring that the profit-sharing rate specified by a licensing contract should not exceed the percentage difference of involved firms’ equilibrium outputs before licensing.     

标准专利许可中可变价格的社会福利效应:基于产品差异化的视角

技术标准在产品生产过程中的使用越来越广泛,标准专利许可定价形式问题关系到技术标准所有者和产品生产者的收益,有待拓展研究。通过构建古诺竞争模型,从产品差异化角度对标准专利许可中可变价格形式的社会福利效应进行分析,得到的主要结论为:当产品市场达到均衡,且标准专利许可采用的价格形式是可变价格时,社会总福利随着产品差异化程度的提高而增加,随着差异化产品市场中标准专利使用者数量的增加而增加,随着可变价格中可变费用比率的提高而降低;均衡产量随着产品差异化程度的提高而增大,随着可变价格中可变费用比率的提高而降低;均衡价格与产品差异化程度呈现出倒“U”型关系,临界点为特定的市场规模;标准专利使用者的均衡利润随着产品差异化程度的提高而增大。由此可见,标准专利许可的可变费用比率下降有利于激励技术标准使用者生产更多的差异化产品,提升社会总福利。     

THE SCOPE FOR COLLUSION AND COMPETITION IN A REGULATED VERTICALLY INTEGRATED INDUSTRY*

This paper investigates the competitive implications of input price controls in a partially regulated industry where a vertically integrated firm has exclusive control over an input with natural monopoly characteristics. Such industry structures are commonly encountered in activities such as telecommunications, railways, electricity and water supply. It is shown that in a Cournot game such input price controls are unambiguously benefical to consumers. However, it is further demonstrated that there exist circumstances in which these controls may make the non-integrated firm worse off. Thus if the objective of input price regulation is to protect the non-integrated firm, such controls may prove to be counterproductive.