scholarly journals Local Stability of Cournot Equilibrium as the Number of Firms Increases

2021 ◽  
pp. 972-980
Author(s):  
Adyda Ibrahim ◽  
Nerda Zura Zaibidi ◽  
Azizan Saaban
Keyword(s):  
Local Stability ◽  
Marginal Cost ◽  
Demand Function ◽  
Cournot Oligopoly ◽  
Cournot Equilibrium ◽  
Adaptive Expectations ◽  
The Third ◽  
Decision Mechanisms ◽  
Isoelastic Demand Function ◽  
Number Of Firms

In this paper, a Cournot oligopoly with isoelastic demand function and constant marginal cost is considered. The local stability conditions of the Cournot equilibrium are determined for four models with different decision mechanisms. In the first model, firms adjust their outputs using the best reply response with naive expectations. The second model is a generalization of the first one, where firms have adaptive expectations. Meanwhile, the third and fourth models adopt the bounded rationality and local monopolistic approximation, respectively. The results show that, in the case of identical firms, the Cournot equilibrium is always stable when the firms adopt the local monopolistic approximation mechanism.

Pricing of Connected and Autonomous Vehicles in Mixed-Traffic Networks

2021 ◽  
pp. 036119812098585
Author(s):  
Paolo Delle Site
Keyword(s):  
Autonomous Vehicles ◽  
Marginal Cost ◽  
User Behavior ◽  
Social Planner ◽  
Traffic Networks ◽  
Mixed Traffic ◽  
The Third ◽  
First Case ◽  
Marginal Cost Pricing ◽  
The Social

For networks with human-driven vehicles (HDVs) only, pricing with arc-specific tolls has been proposed to achieve minimization of travel times in a decentralized way. However, the policy is hardly feasible from a technical viewpoint without connectivity. Therefore, for networks with mixed traffic of HDVs and connected and autonomous vehicles (CAVs), this paper considers pricing in a scenario where only CAVs are charged. In contrast to HDVs, CAVs can be managed as individual vehicles or as a fleet. In the latter case, CAVs can be routed to minimize the travel time of the fleet of CAVs or that of the entire fleet of HDVs and CAVs. We have a selfish user behavior in the first case, a private monopolist behavior in the second, a social planner behavior in the third. Pricing achieves in a decentralized way the social planner optimum. Tolls are not unique and can take both positive and negative values. Marginal cost pricing is one solution. The valid toll set is provided, and tolls are then computed according to two schemes: one with positive tolls only and minimum toll expenditure, and one with both tolls and subsidies and zero net expenditure. Convergent algorithms are used for the mixed-behavior equilibrium (simplicial decomposition algorithm) and toll determination (cutting plane algorithm). The computational experience with three networks: a two-arc network representative of the classic town bypass case, the Nguyen-Dupuis network, and the Anaheim network, provides useful policy insight.

Learning the demand function in a repeated Cournot oligopoly game

2008 ◽  
Vol 39 (4) ◽  
pp. 403-419 ◽  
Author(s):  
Gian-Italo Bischi ◽  
Lucia Sbragia ◽  
Ferenc Szidarovszky
Keyword(s):  
Demand Function ◽  
Cournot Oligopoly

Unequal Treatment of Identical Agents in Cournot Equilibrium

1999 ◽  
Vol 89 (3) ◽  
pp. 585-604 ◽  
Author(s):  
Stephen W Salant ◽  
Greg Shaffer
Keyword(s):  
Marginal Cost ◽  
Consumer Surplus ◽  
Production Costs ◽  
Cournot Equilibrium ◽  
Unequal Treatment ◽  
Marginal Costs ◽  
Second Stage ◽  
Policy Debates ◽  
The Cost ◽  
Antitrust Regulation

Oligopoly models where prior actions by firms affect subsequent marginal costs have been useful in illuminating policy debates in areas such as antitrust regulation, environmental protection, and international competition. We discuss properties of such models when a Cournot equilibrium occurs at the second stage. Aggregate production costs strictly decline with no change in gross revenue or gross consumer surplus if the prior actions strictly increase the variance of marginal costs without changing the marginal-cost sum. Therefore, unless the cost of inducing second-stage asymmetry more than offsets this reduction in production costs, the private and social optima are asymmetric. (JEL D43, L13, L40)

A Few Bad Apples Spoil the Barrel: An Anti-Folk Theorem for Anonymous Repeated Games with Incomplete Information

2020 ◽  
Vol 110 (12) ◽  
pp. 3817-3835
Author(s):  
Takuo Sugaya ◽  
Alexander Wolitzky
Keyword(s):  
Incomplete Information ◽  
Repeated Games ◽  
Prisoner’S Dilemma ◽  
Folk Theorem ◽  
Smoothness Condition ◽  
Cournot Oligopoly ◽  
Random Matching ◽  
Games With Incomplete Information ◽  
Linear Demand ◽  
Number Of Firms

We study anonymous repeated games where players may be “commitment types” who always take the same action. We establish a stark anti-folk theorem: if the distribution of the number of commitment types satisfies a smoothness condition and the game has a “pairwise dominant” action, this action is almost always taken. This implies that cooperation is impossible in the repeated prisoner's dilemma with anonymous random matching. We also bound equilibrium payoffs for general games. Our bound implies that industry profits converge to zero in linear-demand Cournot oligopoly as the number of firms increases. (JEL C72, C73, D83)

GLOBAL BIFURCATIONS IN DUOPOLY WHEN THE COURNOT POINT IS DESTABILIZED VIA A SUBCRITICAL NEIMARK BIFURCATION

2006 ◽  
Vol 08 (01) ◽  
pp. 1-20 ◽  
Author(s):  
ANNA AGLIARI ◽  
LAURA GARDINI ◽  
TONU PUU
Keyword(s):  
Fixed Point ◽  
Equilibrium Point ◽  
Demand Function ◽  
Global Bifurcations ◽  
Cournot Equilibrium ◽  
Oligopoly Model ◽  
Marginal Costs

An adaptive oligopoly model, where the demand function is isoelastic and the competitors operate under constant marginal costs, is considered. The Cournot equilibrium point then loses stability through a subcritical Neimark bifurcation. The present paper focuses some global bifurcations, which precede the Neimark bifurcation, and produce other attractors which coexist with the still attractive Cournot fixed point.

Analysis on Cournot Oligopoly Game Models With Two Firms and More Than Two Firms

2008 ◽  
Author(s):  
Junyan Wang
Keyword(s):  
Nash Equilibrium ◽  
Equilibrium Point ◽  
Cooperative Game ◽  
Pure Strategy ◽  
Cournot Oligopoly ◽  
Cournot Equilibrium ◽  
Cournot Game ◽  
Existence Conditions ◽  
Equilibrium Theorem

This paper reviews the standard game models and its Nash equilibrium and then analyses Cournot oligopoly game from two firms to the case with more than two firms. Due to Cournot equilibrium point, the concept of Cournot equilibrium point is the same as the concept as the non-cooperative game with pure strategy but the strategy can be chosen in Cournot game is infinity and it can not be obtained base on Nash equilibrium theorem. Finally, the existence conditions of Cournot equilibrium point are given and the theorem and its proof of the existence Cournot equilibrium point are given too.

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