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.

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 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.

EFFECTS OF SYMMETRY ON GLOBALIZING SEPARATED MONOPOLIES TO A NASH-COURNOT OLIGOPOLY

2012 ◽  
Vol 14 (02) ◽  
pp. 1250009 ◽  
Author(s):  
HISAO KAMEDA ◽  
TAKASHI UI
Keyword(s):  
Consumer Surplus ◽  
The Other ◽  
Production Functions ◽  
Noncooperative Game ◽  
Cournot Oligopoly ◽  
Worst Case ◽  
Oligopolistic Market ◽  
Complete Symmetry ◽  
Worst Case Ratio ◽  
Linear Demand

The effects of uniting separated markets, each monopolized by a producer, into a globalized oligopolistic market, which is regarded as a noncooperative game, or as a Cournot oligopoly game, are investigated. The cases where such globalization degrades the profits of all producers coincidently, are examined. Linear demand and production functions are considered. It is shown that in complete symmetry, the degree of such coincident profit degradation is strongest (the worst-case ratio), where the degree means the most modest ratio of the profit degradation among all producers. The system is in complete symmetry when the values of parameters describing all producers and markets are identical. On the other hand, in producer symmetry, the degree of coincident consumer surplus improvement is highest (the best-case ratio), where the degree means the lowest of the ratios of consumer surplus improvement among all (previously separated) markets. The system is in producer symmetry when the values of parameters describing all producers are identical.

scholarly journals The Pice Effects of Competition from Parallel Imports and Therapeutic Alternatives: Using Dynamic Models to Estimate the Causal Effect on the Extensive and Intensive Margins

2021 ◽  
Author(s):  
David Granlund
Keyword(s):  
Dynamic Models ◽  
Causal Effect ◽  
The Other ◽  
Causal Effects ◽  
Parallel Imports ◽  
Extensive And Intensive Margins ◽  
Price Effects ◽  
Short And Long Term ◽  
Therapeutic Alternatives

AbstractThis paper studies responses to competition with the use of dynamic models that distinguish between short- and long-term price effects. The dynamic models also allow lagged numbers of competitors to become valid and strong instruments for the current numbers, which enables studying the causal effects using flexible specifications. A first parallel trader is found to decrease prices of exchangeable products by 7% in the long term. On the other hand, prices do not respond to the first competitor that sells therapeutic alternatives; but competition from four or more competitors that sell on-patent therapeutic alternatives decreases prices by about 10% in the long term.

scholarly journals Well-definedness and observational equivalence for inductive–coinductive programs

2019 ◽  
Vol 29 (4) ◽  
pp. 419-468
Author(s):  
Henning Basold ◽  
Helle Hvid Hansen
Keyword(s):  
Fixed Point ◽  
Modal Logic ◽  
The Other ◽  
Observational Equivalence ◽  
Other Hand ◽  
Inductive Types ◽  
Point Types ◽  
Usual Topology

Abstract We define notions of well-definedness and observational equivalence for programs of mixed inductive and coinductive types. These notions are defined by means of tests formulas which combine structural congruence for inductive types and modal logic for coinductive types. Tests also correspond to certain evaluation contexts. We define a program to be well-defined if it is strongly normalizing under all tests, and two programs are observationally equivalent if they satisfy the same tests. We show that observational equivalence is sufficiently coarse to ensure that least and greatest fixed point types are initial algebras and final coalgebras, respectively. This yields inductive and coinductive proof principles for reasoning about program behaviour. On the other hand, we argue that observational equivalence does not identify too many terms, by showing that tests induce a topology that, on streams, coincides with usual topology induced by the prefix metric. As one would expect, observational equivalence is, in general, undecidable, but in order to develop some practically useful heuristics we provide coinductive techniques for establishing observational normalization and observational equivalence, along with up-to techniques for enhancing these methods.

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

Correction to a definition of negation

1984 ◽  
Vol 49 (1) ◽  
pp. 47-50 ◽  
Author(s):  
Frederic B. Fitch
Keyword(s):  
Fixed Point ◽  
Personal Communication ◽  
The Other ◽  
Transfinite Induction ◽  
Original Form ◽  
Basic Logic ◽  
Double Negation ◽  
Original Letter ◽  
The Law ◽  
Definition Of

In [3] a definition of negation was presented for the system K′ of extended basic logic [1], but it has since been shown by Peter Päppinghaus (personal communication) that this definition fails to give rise to the law of double negation as I claimed it did. The purpose of this note is to revise this defective definition in such a way that it clearly does give rise to the law of double negation, as well as to the other negation rules of K′.Although Päppinghaus's original letter to me was dated September 19, 1972, the matter has remained unresolved all this time. Only recently have I seen that there is a simple way to correct the definition. I am of course very grateful to Päppinghaus for pointing out my error in claiming to be able to derive the rule of double negation from the original form of the definition.The corrected definition will, as before, use fixed-point operators to give the effect of the required kind of transfinite induction, but this time a double transfinite induction will be used, somewhat like the double transfinite induction used in [5] to define simultaneously the theorems and antitheorems of system CΓ.

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

scholarly journals A Double Sky-Hook Algorithm for Improving Road-Holding Property in Semi-Active Suspension Systems for Application to In-Wheel Motor

2021 ◽  
Vol 11 (19) ◽  
pp. 8912
Author(s):  
Seunghoon Woo ◽  
Donghoon Shin
Keyword(s):  
Computer Simulations ◽  
Dynamic Models ◽  
Active Suspension ◽  
The Other ◽  
Driving Mode ◽  
The Road ◽  
Suspension Systems ◽  
Active Suspension Systems ◽  
Main Disadvantage ◽  
Advanced Development

This paper presents a double sky-hook algorithm for controlling semi-active suspension systems in order to improve road-holding property for application in an in-wheel motor. The main disadvantage of the in-wheel motor is the increase in unsprung masses, which increases after shaking of the wheel, so it has poor road-holding that the conventional theoretical sky-hook algorithm cannot achieve. The double sky-hook algorithm uses a combination of damper coefficients, one from the chassis motion and the other from the wheel motion. Computer simulations using a quarter and full car dynamic models with the road conditions specified by ISO2631 showed the effectiveness of the algorithm. It was observed that the algorithm was the most effective in the vicinity of the wheel hop frequency. This paper also proposed the parameter set of the double sky-hook algorithm to differentiate the driving mode of vehicles under advanced development.

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