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.     

Diagrammatic Demonstration of the Cournot Equilibrium

This note further develops Ikema's (1990, 1991) diagrammatic demonstrati on of the Cournot-oligopoly equilibrium on the price- quantity plane. It is shown that Ikema's method can be used to illustrate the Stackelberg and Bertrand equilibria on the price- quantity plane. Furthermore, we algebraically derive the ``monopoly- equilibrium' curve and show that the Cournot- oligopoly equilibrium is stable if the monopoly-equilibrium curves for all producers are upward sloping.     

Bertrand versus Cournot revisited

Summary. Bertrand criticized Cournot's analysis of the competitive process, arguing that firms should be seen as playing a strategy of setting price below competitors' prices (henceforth, the Bertrand strategy) instead of a strategy of accepting the price needed to sell an optimal quantity (the Cournot strategy). We characterize Nash equilibria in a generalized model in which firms choose among Cournot and Bertrand strategies. Best responses always exist in this model. For the duopoly case, we show that iterated best responses converge under mild assumptions on initial states either to Cournot equilibrium or to an equilibrium in which only one firm plays the Bertrand strategy with price equal to marginal cost and that firm has zero sales. Received: December 11, 1995; revised version October 2, 1996     

The effect of product differentiation on dynamic Cournot and Stackelberg stability

A model of competition in a market is given when product differentiation occurs. Weighting factors are introduced in both demand and cost functions. The dynamics of the system are studied under the assumptions of Cournot and Stackelberg strategies. The effects of the weighting factors upon stability are specifically studied in some detail.     

Is a Unique Cournot Equilibrium Locally Stable?

We consider a homogeneous product oligopoly, where the Cournot equilibrium is regular and unique. We show that for a duopoly, a unique Cournot equilibrium is always locally stable. For a “n” firm asymmetric cost oligopoly a unique Cournot equilibrium is locally stable under very general conditions. The sufficient conditions for local stability of a unique Cournot equilibrium are much less restrictive than what the existing literature suggests. For a symmetric cost oligopoly the unique Cournot equilibrium is almost always locally stable, except for a perverse case. Journal of Economic Literature Classification number: L13.     

Stackelberg Beats Cournot — On Collusion and Efficiency in Experimental Markets

We report on an experiment designed to compare Stackelberg and Cournot duopoly markets with quantity competition. We implement both a random matching and a fixed-pairs version for each market. Stackelberg markets yield, regardless of the matching scheme, higher outputs than Cournot markets and, thus, higher efficiency. For Cournot markets, we replicate a pattern known from previous experiments. There is stable equilibrium play under random matching and partial collusion under fixed pairs. We also find, for Stackelberg markets, that competition becomes less intense when firms remain in pairs but we find considerable deviations from the subgame perfect equilibrium prediction which can be attributed to an aversion to disadvantageous inequality.     

Equilibrium prices in the Bertrand and Cournot oligopolies

The equilibrium prices for the Bertrand and Cournot oligopolies with product differentiation are compared. If all firms have linear demand and cost functions, and if, in addition, the Jacobian matrix of the demand functions has a dominant negative diagonal, the Cournot equilibrium prices are not lower than the Bertrand ones. The general condition for the comparison of the Bertrand and Cournot equilibrium prices can be derived even if the nonlinearity is involved in the cost and/or demand functions.     

Public Input Competition under Stackelberg Equilibrium: A Note

This paper examines the Stackelberg equilibrium for public input competition and compares it with the noncooperative Nash equilibrium. Given two asymmetric regions, we show that under the Nash equilibrium the more productive region tends to spend more on public input, which results in this region attracting more capital than the less productive region. The comparison of the two equilibria reveals that the leader region obtains a first‐mover advantage under the Stackelberg setting. This suggests that if regions interact with each other sequentially as in the Stackelberg equilibrium, then the regional disparity that is due to the heterogeneity of productivity is likely to be mitigated or enlarged, depending on which region performs the leadership role in the competition process.     

基于同时博弈和序贯博弈的寡头市场古诺均衡比较分析

根据国内外在古诺模型研究上的缺陷,分别从古诺假定、产品差异、成本差异以及非线性市场需求等方面对垄断市场结构中厂商之间同时博弈与序贯博弈两种情况的均衡状况进行比较分析,得出寡头垄断市场中厂商之间的均衡与产品质量、成本状况、市场需求以及博弈的顺序等因素有关的结论,从而为中国相关行业的决策提供理论依据。     

Free Trade versus Autarky under Asymmetric Cournot Oligopoly

The paper compares free trade with autarky in an asymmetric multi‐country world under Cournot competition with constant returns to scale and linear demand. We derive respective conditions under which free trade will hurt a country's consumers, benefit its firms, induce it to export, increase its output and raise its welfare. We show that these conditions are linked in a clear order, with one implying the next. We further demonstrate that free trade can reduce world total output and total consumer surplus as well as world welfare. Along the way, we correct several oversights in the literature.     

On the Uniqueness of Equilibrium in Cournot Oligopoly and Other Games

In an average surplus sharing game, such as a Cournot oligopoly, a group of agents share a production process. Each contributes an amount of input to the process, and output is divided in proportion to the amount of input contributed. Uniqueness of the equilibrium is needed for any type of comparative static analysis. However, general uniqueness results for concave games have restrictive assumptions on preferences and technology; specifically, the conditions needed for uniqueness become more difficult to meet as the number of players increases. A new theorem for uniqueness with easily interpretable conditions is given which is independent of the number of players.Journal of Economic LiteratureClassification Numbers: C70, C72, D43.     

Outsourcing versus technology transfer: Hotelling meets Stackelberg

We consider a Hotelling duopoly with two firms $A$ and $B$ in the final good market. Both can produce the required intermediate good, firm $B$ having a lower cost due to a superior technology. We compare two contracts: outsourcing ( $A$ orders the intermediate good from $B$ ) and technology transfer ( $B$ transfers its technology to $A$ ). An outsourcing order is equivalent to building an endogenous capacity and it generates a Stackelberg leadership effect for firm $A,$ which is absent in technology transfer. We show that compared to the situation of no contracts there are always Pareto improving outsourcing contracts (making both firms better off and all consumers at least weakly better off), but no Pareto improving technology transfer contracts. It is also shown that if firm $B$ has a relatively large bargaining power in its negotiations with $A,$ then both firms prefer technology transfer while all consumers prefer outsourcing.     

Unit versus Ad Valorem Taxes in Multiproduct Cournot Oligopoly

The welfare dominance of ad valorem taxes over unit taxes in a single‐market Cournot oligopoly is well known. This article extends the analysis to multimarket oligopoly. Provided all ad valorem taxes are equal and positive, unit costs are constant, firms are active in all considered markets, and a representative consumer has convex preferences, ad valorem taxes are shown to dominate in multiproduct equilibrium. Conditions exist, however, under which economic efficiency declines upon replacing specific taxes with ad valorem taxes that preserve output levels. We discuss the roles of unit cost covariances across multiproduct firms, and also of complementarity in demand, in determining the extent of cost efficiencies arising under ad valorem taxation. For goods that are complementary or independent in demand, conditions are found such that industry profits decline upon use of ad valorem taxes.     

Technology adoption in a differentiated duopoly: Cournot versus Bertrand

This paper shows that the cost as well as the effectiveness of technology has a differential impact on technology adoption under two alternative modes of competition. If the cost of the technology is high, Bertrand competition provides a stronger incentive to adopt technology than Cournot competition unless the effectiveness of the technology is very low. On the contrary, if the cost of the technology is low, Cournot competition fares better than Bertrand competition in terms of technology adoption by firms. This demonstrates that the commonly subscribed assumption of ‘positive primary outputs’ restricts (inflates) the scope of higher degree of technology adoption under Bertrand (Cournot) competition. Moreover, in contrast to standard welfare ranking, it shows that Cournot competition leads to higher social welfare than Bertrand competition under certain situations.     

A note on merger in mixed duopoly: Bertrand versus Cournot

In this note we analyze the incentives to merge in a mixed duopoly if firms compete in prices or quantities. Our model framework mainly follows Barcena-Ruiz and Garzon (J Econ 80:27–42, 2003) who set up the model with quantity competition. We extend their analysis by analyzing the case of competition in prices. Further we compare the incentives to merge with Bertrand and Cournot competition. Comparing quantity with price competition we can show that a merger is more likely with Cournot competition than with Bertrand competition.     

Dynamic efficiency of Cournot and Bertrand competition: input versus output spillovers

We consider the efficiency of Cournot and Bertrand equilibria in a duopoly with substitutable goods where firms invest in process R&D that generates input spillovers. Under Cournot competition firms always invest more in R&D than under Bertrand competition. More importantly, Cournot competition yields lower prices than Bertrand competition when the R&D production process is efficient, when spillovers are substantial, and when goods are not too differentiated. The range of cases for which total surplus under Cournot competition exceeds that under Bertrand competition is even larger as competition over quantities always yields the largest producers’ surplus.     

Bertrand versus Cournot competition in a downstream mixed oligopoly with foreign ownership

Focusing on foreign ownership in the private firm, we examine the Cournot-Bertrand comparison in a mixed oligopolistic market with vertical market structure. We have found that if public and private firms were charged with uniform price for their inputs, then Cournot-Bertrand ranking in market outcomes confirms those obtained by Ghosh and Mitra (2010). This implies that under uniform pricing in the upstream sector, the vertical market structure does not have substantial influences on Cournot-Bertrand ranking. However, if discriminatory pricing is adopted, firm's profits, output, and social welfare are often reversed to those obtained from uniform pricing in the upstream sector. Given the closeness of products, if the share of foreign ownership is sufficiently low, social welfare in Cournot competition can exceed that of Bertrand competition, contrasting with the standard welfare ranking that Bertrand welfare is strictly higher than Cournot. This implies that Cournot competition can be more socially desirable than Bertrand in mixed oligopoly with vertical market structure if discriminatory pricing scheme is adopted by foreign upstream monopolists.     

Majority Voting in Multidimensional Policy Spaces: Kramer–Shepsle versus Stackelberg

We study majority voting over a bidimensional policy space when the voters’ type space is either uni‐ or bidimensional. We study two voting procedures widely used in the literature. The Stackelberg (ST) procedure assumes that votes are taken one dimension at a time according to an exogenously specified sequence. The Kramer–Shepsle (KS) procedure also assumes that votes are taken separately on each dimension, but not in a sequential way. A vector of policies is a Kramer–Shepsle equilibrium if each component coincides with the majority choice on this dimension given the other components of the vector. We study the existence and uniqueness of the ST and KS equilibria, and we compare them, looking for example at the impact of the ordering of votes for ST and identifying circumstances under which ST and KS equilibria coincide. In the process, we state explicitly the assumptions on the utility function that are needed for these equilibria to be well‐behaved. We especially stress the importance of single‐crossing conditions, and we identify two variants of these assumptions: a marginal version that is imposed on all policy dimensions separately, and a joint version whose definition involves both policy dimensions.     

Leibniz und Cournot

Ohne Zusammenfassung