Asymptotic Convergence to Competitive Equilibrium of Oligopoly Equilibria

2010 ◽  
Author(s):  
Somdeb Lahiri
Keyword(s):  
Competitive Equilibrium ◽  
Asymptotic Convergence

scholarly journals The Issue of Macroeconomic Closure Revisited and Extended

2016 ◽  
Vol 66 (1) ◽  
pp. 1-31
Author(s):  
Ernő Zalai ◽  
Tamás Révész
Keyword(s):  
General Equilibrium ◽  
Open Economy ◽  
Computable General Equilibrium ◽  
Statistical Data ◽  
Competitive Equilibrium ◽  
Numerical Models ◽  
Cge Model ◽  
Sector Model ◽  
Cge Models ◽  
Policy Simulations

Léon Walras (1874) had already realised that his neo-classical general equilibrium model could not accommodate autonomous investments. In the early 1960s, Amartya Sen analysed the same issue in a simple, one-sector macroeconomic model of a closed economy. He showed that fixing investment in the model, built strictly on neo-classical assumptions, would make the system overdetermined, and thus one should loosen some neo-classical conditions of competitive equilibrium. He analysed three not neo-classical “closure options”, which could make the model well-determined in the case of fixed investment. His list was later extended by others and it was shown that the closure dilemma arises in the more complex computable general equilibrium (CGE) models as well, as does the choice of adjustment mechanism assumed to bring about equilibrium at the macro level. It was also illustrated through several numerical models that the adopted closure rule can significantly affect the results of policy simulations based on a CGE model. Despite these warnings, the issue of macro closure is often neglected in policy simulations. It is, therefore, worth revisiting the issue and demonstrating by further examples its importance, as well as pointing out that the closure problem in the CGE models extends well beyond the problem of how to incorporate autonomous investments into a CGE model. Several closure rules are discussed in this paper and their diverse outcomes are illustrated by numerical models calibrated on statistical data. First, the analyses are done in a one-sector model, similar to Sen’s, but extended into a model of an open economy. Next, the same analyses are repeated using a fully-fledged multi-sectoral CGE model, calibrated on the same statistical data. Comparing the results obtained by the two models it is shown that although they generate quite similar results in terms of the direction and — to a somewhat lesser extent — of the magnitude of change in the main macro variables using the same closure option, the predictions of the multi-sectoral CGE model are clearly more realistic and balanced.

scholarly journals Holding a group together: non-game-theory vs. game-theory

2021 ◽  
Author(s):  
Michael Richter ◽  
Ariel Rubinstein
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Competitive Equilibrium ◽  
Solution Concept ◽  
Equilibrium Concept

Abstract Each member of a group chooses a position and has preferences regarding his chosen position. The group’s harmony depends on the profile of chosen positions meeting a specific condition. We analyse a solution concept (Richter and Rubinstein, 2020) based on a permissible set of individual positions, which plays a role analogous to that of prices in competitive equilibrium. Given the permissible set, members choose their most preferred position. The set is tightened if the chosen positions are inharmonious and relaxed if the restrictions are unnecessary. This new equilibrium concept yields more attractive outcomes than does Nash equilibrium in the corresponding game.

scholarly journals Regularized Asymptotics of the Solution of the Singularly Perturbed First Boundary Value Problem on the Semiaxis for a Parabolic Equation with a Rational “Simple” Turning Point

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 405
Author(s):  
Alexander Yeliseev ◽  
Tatiana Ratnikova ◽  
Daria Shaposhnikova
Keyword(s):  
Parabolic Equation ◽  
Maximum Principle ◽  
Boundary Value Problem ◽  
Regularization Method ◽  
Turning Point ◽  
Boundary Value ◽  
Singularly Perturbed ◽  
Asymptotic Convergence ◽  
The Maximum Principle ◽  
Regularized Asymptotics

The aim of this study is to develop a regularization method for boundary value problems for a parabolic equation. A singularly perturbed boundary value problem on the semiaxis is considered in the case of a “simple” rational turning point. To prove the asymptotic convergence of the series, the maximum principle is used.

The effect of a footprint on perceived surface roughness

1986 ◽  
Vol 405 (1829) ◽  
pp. 303-327 ◽  
Keyword(s):  
Surface Roughness ◽  
Weighting Function ◽  
Sampling Interval ◽  
Asymptotic Convergence ◽  
Reference Surface ◽  
Two Dimensional ◽  
Random Surface ◽  
Spectral Density Functions ◽  
Continuous Theory ◽  
Discrete Theory

A two-dimensional homogeneous random surface { y ( X )} is generated from another such surface { z ( X )} by a process of smoothing represented by y ( X ) = ∫ ∞ d u w ( u – X ) z ( u ), where w ( X ) is a deterministic weighting function satisfying certain conditions. The two-dimensional autocorrelation and spectral density functions of the smoothed surface { y ( X )} are calculated in terms of the corresponding functions of the reference surface { z ( X )} and the properties of the ‘footprint’ of the contact w ( X ). When the surfaces are Gaussian, the statistical properties of their peaks and summits are given by the continuous theory of surface roughness. If only sampled values of the surface height are available, there is a corresponding discrete theory. Provided that the discrete sampling interval is small enough, profile statistics calculated by the discrete theory should approach asymptotically those calculated by the continuous theory, but it is known that such asymptotic convergence may not occur in practice. For a smoothed surface { y ( X )} which is generated from a reference surface { z ( X )} by a ‘good’ footprint of finite area, it is shown in this paper that the expected asymptotic convergence does occur always, even if the reference surface is ideally white. For a footprint to be a good footprint, w ( X ) must be continuous and smooth enough that it can be differentiated twice everywhere, including at its edges. Sample calculations for three footprints, two of which are good footprints, illustrate the theory.

scholarly journals Optimality of a Competitive Equilibrium in a Small Open City with Congestion

1998 ◽  
Vol 43 (2) ◽  
pp. 181-198 ◽  
Author(s):  
Nobuo Akai ◽  
Takashi Fukushima‡ ◽  
Tatsuo Hatta
Keyword(s):  
Competitive Equilibrium
Sign in / Sign up

Export Citation Format

Share Document