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.

scholarly journals Rational expectations and the Cournot-Theocharis problem

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Tönu Puu
Keyword(s):  
Fixed Point ◽  
Rational Expectations ◽  
Demand Function ◽  
Dynamic Models ◽  
The Other ◽  
Cournot Oligopoly ◽  
Trivial Case ◽  
Oligopoly Model ◽  
Marginal Costs ◽  
Linear Demand

In dynamic models in economics, often “rational expectations” are assumed. These are meant to show that the agents can correctly foresee the result of their own and the other agents' actions. In this paper, it is shown that this cannot happen in a simple oligopoly model with a linear demand function and constant marginal costs. “Naive expectations,” that is, where each agent assumes the other agents to retain their previous period action, are shown to result in a 2-period cycle. However, adapting to the observed periodicity always doubles the actual resulting periodicity. In general, it is impossible for the agents to learn any periodicity except the trivial case of a fixed point. This makes the whole idea of “rational expectations” untenable in Cournot oligopoly models.

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)

scholarly journals Further Investigations on the Dynamics and Multistability Coexisted in a Memory-Based Cobweb Model

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
S. S. Askar
Keyword(s):  
Fixed Point ◽  
Equilibrium Point ◽  
Profit Maximization ◽  
Period Doubling ◽  
Speed Of Adjustment ◽  
Discrete Dynamic ◽  
Cobweb Model ◽  
Numerical Studies ◽  
Market Clearing Price ◽  
The Stability

Based on a nonlinear demand function and a market-clearing price, a cobweb model is introduced in this paper. A gradient mechanism that depends on the marginal profit is adopted to form the 1D discrete dynamic cobweb map. Analytical studies show that the map possesses four fixed points and only one attains the profit maximization. The stability/instability conditions for this fixed point are calculated and numerically studied. The numerical studies provide some insights about the cobweb map and confirm that this fixed point can be destabilized due to period-doubling bifurcation. The second part of the paper discusses the memory factor on the stabilization of the map’s equilibrium point. A gradient mechanism that depends on the marginal profit in the past two time steps is adopted to incorporate memory in the model. Hence, a 2D discrete dynamic map is constructed. Through theoretical and numerical investigations, we show that the equilibrium point of the 2D map becomes unstable due to two types of bifurcations that are Neimark–Sacker and flip bifurcations. Furthermore, the influence of the speed of adjustment parameter on the map’s equilibrium is analyzed via numerical experiments.

COMPLEXITY OF A REAL ESTATE GAME MODEL WITH A NONLINEAR DEMAND FUNCTION

2011 ◽  
Vol 21 (11) ◽  
pp. 3171-3179 ◽  
Author(s):  
LINGLING MU ◽  
PING LIU ◽  
YANYAN LI ◽  
JINZHU ZHANG
Keyword(s):  
Nash Equilibrium ◽  
Real Estate ◽  
Equilibrium Point ◽  
Demand Function ◽  
Control Method ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Game Model ◽  
Nonlinear Feedback ◽  
Nash Equilibrium Point

In this paper, a real estate game model with nonlinear demand function is proposed. And an analysis of the game's local stability is carried out. It is shown that the stability of Nash equilibrium point is lost through period-doubling bifurcation as some parameters are varied. With numerical simulations method, the results of bifurcation diagrams, maximal Lyapunov exponents and strange attractors are presented. It is found that the chaotic behavior of the model has been stabilized on the Nash equilibrium point by using of nonlinear feedback control method.

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.

scholarly journals Critical bifurcation surfaces of 3D discrete dynamics

2000 ◽  
Vol 4 (4) ◽  
pp. 333-343 ◽  
Author(s):  
Michael Sonis
Keyword(s):  
Fixed Point ◽  
Asymptotic Stability ◽  
Bifurcation Analysis ◽  
Analytical Representation ◽  
General Algorithm ◽  
Cournot Oligopoly ◽  
Adjustment Process ◽  
Discrete Dynamics ◽  
Oligopoly Model ◽  
Analytical Construction

This paper deals with the analytical representation of bifurcations of each 3D discrete dynamics depending on the set of bifurcation parameters. The procedure of bifurcation analysis proposed in this paper represents the 3D elaboration and specification of the general algorithm of then-dimensional linear bifurcation analysis proposed by the author earlier. It is proven that 3D domain of asymptotic stability (attraction) of the fixed point for a given 3D discrete dynamics is bounded by three critical bifurcation surfaces: the divergence, flip and flutter surfaces. The analytical construction of these surfaces is achieved with the help of classical Routh–Hurvitz conditions of asymptotic stability. As an application the adjustment process proposed by T. Puu for the Cournot oligopoly model is considered in detail.

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