Asymmetric equilibria under price cap regulation

This study analyzes the effects of a price-cap regulation on market outcomes in Cournot and Stackelberg duopolies. Although two firms are ex-ante identical, there are asymmetric Cournot equilibria as well as the symmetric equilibrium under the price-cap regulation, when the price-cap level is binding. By contrast, the Stackelberg equilibrium is unique and equivalent to the most asymmetric Cournot equilibrium under a binding price-cap level. We present several comparative statics results with respect to the equilibrium outcomes. The main concern of this study is the welfare effect of a change in a price-cap level. We show that when asymmetric Cournot equilibria or the Stackelberg equilibrium are focused on, a reduction in a price-cap level may be socially harmful even if the price-cap level is more than the competitive price.     

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.     

Non-renewable resource Stackelberg games

The market structure for many mineral industries can be described as oligopoly with potential for Stackelberg leadership. This paper derives and analyzes dynamically consistent extraction equilibria in a two-period discrete-time “Truly” Stackelberg (TS) model of non-renewable resource extraction, where firms move sequentially within each period and where both the leader and follower have market power. We show how the leader may be able to manipulate extraction patterns by exploiting resource constraints. Whether the leader wants to speed up its own production relative to the Cournot–Nash (CN) equilibrium depends on the shape of its iso-profit curve, which is affected by the two firms’ relative stock endowments and relative production costs. If the leader extracts faster, then the follower extracts slower, but in aggregate the industry extracts faster. Unlike static Stackelberg games, the follower does not necessarily have a second mover disadvantage.     

MARKET PRICE MECHANISMS AND STACKELBERG GENERAL EQUILIBRIA: AN EXAMPLE

This paper considers Stackelberg competition in a general equilibrium framework with a productive sector. The working of market power and the configurations of strategic interactions are complexified by the presence of a leader. Two market price mechanisms are studied: one is associated with the Stackelberg–Walras equilibrium and the other is linked to the Stackelberg–Cournot equilibrium. Throughout the example of a two commodity economy, several results are obtained about equilibria mergings and about welfare comparisons.     

Learning to collude: An experiment in convergence and equilibrium selection in oligopoly

The paper considers a simple oligopoly model where firms know their own and the average pay-off in the industry. Firms choose decision rules for trading. The theory predicts that there are three types of Nash equilibria in this game (collusive, Cournot and Stackelberg). Our experiments test the selection process. We find that there is clear evidence of convergence to an equilibrium, and whilst both Cournot and collusive outcomes were selected, the collusive equilibrium is more common. The experimental results also give insights into the process of individual learning, confirming that subjects follow aspiration rules rather than reinforcement rules.     

Pricing decisions in a dual channels system with different power structures

This paper investigates the effect of product substitutability and relative channel status on pricing decisions under different power structures of a dual exclusive channel system where each manufacturer distributes its goods through a single exclusive retailer but two goods are substitute. A linear demand based on the utility function of a representative consumer is assumed, and three game scenarios(Manufacturer Stackelberg, Retailer Stackelbeg and Vertical Nash) are examined under symmetric and asymmetric related channel status. It is shown that no power structure is always the best for the entire supply chain though all members on supply chain have incentive to lead the Stackelberg game. Meanwhile, the vertical Nash game is an equilibrium for the members, however, a Prisoner's dilemma necessarily incurs for the entire supply chain because the Retailer Stackelberg or the Manufacturer Stackelberg can gain the better performance than that in vertical Nash for the entire supply chain when the product substitutability is moderate or higher and the asymmetric relative channel status is moderate, while consumers always get the most welfare from the vertical Nash game.     

On the Frequency of Interior Cournot–Nash Equilibria in a Public Good Economy

In a public good economy the distribution of initial income is an important determinant of how many individuals contribute to the public good in Cournot–Nash equilibrium. In this paper, first a simple formula is derived that provides a measure for the size of the set of income distributions leading to an interior Cournot–Nash equilibrium in which all individuals contribute to the public good. Furthermore, we give an estimate for the frequency that all members of a certain subgroup of the population are contributors.     

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.     

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.     

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 trade paradox persists under excise taxes

Brander and Krugman (1983) and Sertel (1988) followed by Krugman (1989), showed two sides of a ‘trade paradox’: The paradox in competition, viz. that opening trade (or increasing competition) may cause welfare to decline, and the paradox in efficiency, viz. that an increase in unit transport cost may increase welfare. In this paper, we consider the situation in an environment where interventionist trade policies are not permitted but each country is sovereign to impose an excise tax (or subsidy). The paradoxes persist under equilibrium excise taxes, reckoned both at the non-cooperative (Nash or dominant strategy) equilibrium and at the cooperative solution among tax-imposing authorities maximizing welfare. We also see that the paradoxes persist in a taxless environment where market equilibrium is Stackelberg rather than Cournot.     

Patterns of power: bargaining and incentives in two-person games

We introduce the concept of a strategic dictator and use it to analyse patterns of power in two- person games that arise naturally in bargaining, arbitration, and incentive problems. A strategic dictator is an agent who has the power to ensure that a Nash equilibrium outcome is his or her preferred outcome, but who may have to lie in order to do this. We discuss applications of our analysis to Stackelberg and Cournot Duopolists, to bargaining situations, and to the existence of appropriate incentive systems.     

A Two-stage Cournot Duopoly with Inventory Costs

This paper analyses the Cournot duopoly model which has two production periods before the market clears. As shown by Saloner (1987), if inventory costs are zero, many outcomes including both Cournot and Stackelberg outcomes are subgame perfect equilibrium outcomes. However, if small inventory costs are introduced, the Cournot outcome is no longer found in equilibrium and the equilibrium outcomes are only of Stackelberg-type. This suggests that more attention should be paid to the Stackelberg model than to the Cournot model.     

A note on Stackelberg competition

This note investigates a Stackelberg–Nash competition model. We determine the conditions under which the leaders may achieve better profits than the followers when all firms compete on quantity in a two stage game. We focus on the properties of the followers’ best response functions. It is shown that the Stackelberg equilibrium may coincide with the Cournot equilibrium. In addition, the followers may achieve higher profits than the leaders. Such results put forward the working and the consequences of strategic complementarities. These results are illustrated with three examples.     

An experiment on learning with limited information: nonconvergence, experimentation cascades, and the advantage of being slow

We present the results of an experiment on learning in a continuous-time low-information setting. For a dominance solvable version of a Cournot oligopoly with differentiated products, we find little evidence of convergence to the Nash equilibrium. In an asynchronous setting, characterized by players updating their strategies at different frequencies, play tends toward the Stackelberg outcome which favors the slower player. Convergence is significantly more robust for a “serial cost sharing” game, which satisfies a stronger solution concept of overwhelmed solvability. As the number of players grows, this improved convergence tends to diminish, seemingly driven by frequent and highly structured experimentation by players leading to a cascading effect in which experimentation by one player induces experimentation by others. These results have implications both for traditional oligopoly competition and for a wide variety of strategic situations arising on the Internet.     

FDI视角:跨国厂商技术研发量的经济模型分析

文章通过构建一个"研发一生产"两阶段博弈模型,在FDI背景下分别以Cournot竞争模式、Stackelberg竞争模式和Collusion竞争模式研究了东道国市场规模、东道国厂商工资水平以及东道国厂商技术研发量对跨国厂商技术研发量的影响.研究发现,在三种竞争模式下,东道国市场规模对跨国厂商技术研发量都是正向的影响;在Cournot竞争模式和Stackelberg竞争模式下,东道国工资水平对跨国厂商技术研发量也是正向的影响,而在Collusion竞争模式下,东道国工资水平对跨国厂商技术研发量的影响则视产量效果与替代效果的相对大小而定;在Cournot竞争模式和Stackelberg竞争模式下,东道国厂商技术研发量的增加反向影响跨国厂商技术研发量,而在Collusion竞争模式下,东道国厂商技术研发量则不影响跨国厂商技术研发量.     

OWNERSHIP VERSUS TIMING OF THE GAME

This study examines the impact of timing of the game on the welfare gains of privatisation in the presence of strategic trade policy. We argue that only if the public enterprise acts as a Cournot player will it generate an additional distortion that could outweigh the distortion caused by the oligopolistic behaviour of private firms. But with a first-mover advantage it can serve as an effective regulatory device comparable with a production subsidy. We further show that, in the presence of strategic trade policy, Cournot assumptions are inconsistent with the firms' preferences over the timing of the game. As public Stackelberg leadership is a subgame Nash equilibrium of the extended game with endogenous order of moves, we conclude that it is the timing of the game rather than firms' ownership structure which is responsible for the inefficiency of an international mixed market found by earlier studies.     

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.     

Voracity, growth, and welfare

This paper explores some implications of the comparison between feedback Nash and Stackelberg equilibria for growth and welfare in a ‘voracity’ model. We show that, as compared to the Nash equilibrium, the Stackelberg equilibrium involves a lower growth rate, while it leaves both the leaders and the followers better off, i.e., the Stackelberg equilibrium is Pareto superior to the Nash equilibrium.     

On price taking behavior in a nonrenewable resource cartel–fringe game

We consider a nonrenewable resource game with one cartel and a set of fringe members. We show that (i) the outcomes of the closed-loop and the open-loop nonrenewable resource game with the fringe members as price takers (the cartel–fringe game à la Salant, 1976) coincide and (ii) when the number of fringe firms becomes arbitrarily large, the equilibrium outcome of the closed-loop Nash game does not coincide with the equilibrium outcome of the closed-loop cartel–fringe game. Thus, the outcome of the cartel–fringe open-loop equilibrium can be supported as an outcome of a subgame-perfect equilibrium. However the interpretation of the cartel–fringe model, where from the outset the fringe is assumed to be price taker, as a limit case of an asymmetric oligopoly with the agents playing Nash–Cournot, does not extend to the case where firms can use closed-loop strategies.