On Existence and Uniqueness of Equilibrium in Noisy Rational Expectations Economies

2012 ◽  
Author(s):  
Bradyn M. Breon-Drish
Keyword(s):  
Existence And Uniqueness ◽  
Rational Expectations ◽  
Uniqueness Of Equilibrium ◽  
Noisy Rational Expectations

ALMOST ADDITIVE THERMODYNAMIC FORMALISM: SOME RECENT DEVELOPMENTS

2010 ◽  
Vol 22 (10) ◽  
pp. 1147-1179 ◽  
Author(s):  
LUIS BARREIRA
Keyword(s):  
Variational Principle ◽  
Existence And Uniqueness ◽  
Gibbs Measures ◽  
Thermodynamic Formalism ◽  
Topological Pressure ◽  
Present Stage ◽  
The Past ◽  
Recent Developments ◽  
General Sequences ◽  
Uniqueness Of Equilibrium

This is a survey on recent developments concerning a thermodynamic formalism for almost additive sequences of functions. While the nonadditive thermodynamic formalism applies to much more general sequences, at the present stage of the theory there are no general results concerning, for example, a variational principle for the topological pressure or the existence of equilibrium or Gibbs measures (at least without further restrictive assumptions). On the other hand, in the case of almost additive sequences, it is possible to establish a variational principle and to discuss the existence and uniqueness of equilibrium and Gibbs measures, among several other results. After presenting in a self-contained manner the foundations of the theory, the survey includes the description of three applications of the almost additive thermodynamic formalism: a multifractal analysis of Lyapunov exponents for a class of nonconformal repellers; a conditional variational principle for limits of almost additive sequences; and the study of dimension spectra that consider simultaneously limits into the future and into the past.

scholarly journals On the Existence and Uniqueness of Equilibrium in the Bottleneck Model with Atomic Users

2017 ◽  
Vol 51 (3) ◽  
pp. 863-881 ◽  
Author(s):  
Hugo E. Silva ◽  
Robin Lindsey ◽  
André de Palma ◽  
Vincent A. C. van den Berg
Keyword(s):  
Existence And Uniqueness ◽  
Bottleneck Model ◽  
Uniqueness Of Equilibrium

EXISTENCE AND UNIQUENESS OF EQUILIBRIUM IN ASYMMETRIC CONTESTS WITH ENDOGENOUS PRIZES

2013 ◽  
Vol 15 (01) ◽  
pp. 1350005 ◽  
Author(s):  
SHUMEI HIRAI ◽  
FERENC SZIDAROVSZKY
Keyword(s):  
Nash Equilibrium ◽  
Existence And Uniqueness ◽  
Financial Constraints ◽  
Pure Nash Equilibrium ◽  
Asymmetric Contests ◽  
Uniqueness Of Equilibrium

This paper considers contests in which the efforts of the players determine the value of the prize. Players may have different valuations of the prize and different abilities to convert expenditures to productive efforts. In addition, players may face different financial constraints. This paper presents a proof for the existence and uniqueness of a pure Nash equilibrium in asymmetric contests with endogenous prizes.

scholarly journals Equilibrium states for a class of skew products

2019 ◽  
Vol 40 (11) ◽  
pp. 3030-3050
Author(s):  
MARIA CARVALHO ◽  
SEBASTIÁN A. PÉREZ
Keyword(s):  
Existence And Uniqueness ◽  
Global Analysis ◽  
American Mathematical Society ◽  
Sufficient Conditions ◽  
Equilibrium States ◽  
Axiom A ◽  
Skew Products ◽  
Pure Mathematics ◽  
Partially Hyperbolic ◽  
Uniqueness Of Equilibrium

We consider skew products on $M\times \mathbb{T}^{2}$, where $M$ is the two-sphere or the two-torus, which are partially hyperbolic and semi-conjugate to an Axiom A diffeomorphism. This class of dynamics includes the open sets of $\unicode[STIX]{x1D6FA}$-non-stable systems introduced by Abraham and Smale [Non-genericity of Ł-stability. Global Analysis (Proceedings of Symposia in Pure Mathematics, XIV (Berkeley 1968)). American Mathematical Society, Providence, RI, 1970, pp. 5–8.] and Shub [Topological Transitive Diffeomorphisms in$T^{4}$ (Lecture Notes in Mathematics, 206). Springer, Berlin, 1971, pp. 39–40]. We present sufficient conditions, both on the skew products and the potentials, for the existence and uniqueness of equilibrium states, and discuss their statistical stability.

scholarly journals Extendability of Equilibria of Nematic Polymers

2008 ◽  
Vol 2008 ◽  
pp. 1-10
Author(s):  
Hongyun Wang ◽  
Hong Zhou
Keyword(s):  
Nonlinear System ◽  
Existence And Uniqueness ◽  
Jacobian Matrix ◽  
Intersection Point ◽  
Equilibrium States ◽  
Intermolecular Potential ◽  
Small Perturbations ◽  
Nematic Polymers ◽  
Folding Point ◽  
Uniqueness Of Equilibrium

The purpose of this paper is to study the extendability of equilibrium states of rodlike nematic polymers with the Maier-Saupe intermolecular potential. We formulate equilibrium states as solutions of a nonlinear system and calculate the determinant of the Jacobian matrix of the nonlinear system. It is found that the Jacobian matrix is nonsingular everywhere except at two equilibrium states. These two special equilibrium states correspond to two points in the phase diagram. One point is the folding point where the stable prolate branch folds into the unstable prolate branch; the other point is the intersection point of the nematic branch and the isotropic branch where the unstable prolate state becomes the unstable oblate state. Our result establishes the existence and uniqueness of equilibrium states in the presence of small perturbations away from these two special equilibrium states.

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