Optimality Properties of Equilibrium

Florenzano, Monique

doi:10.1007/978-1-4757-5315-8_4

Cited by 5 publications

(2 citation statements)

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“…Then, by using this social equilibrium existence theorem, Arrow and Debreu [2] proved the existence of a general equilibrium for a competitive economy with productions. See Debreu [12] and Florenzano [16] for excellent treatments of the existence of equilibrium. See also Duppe and Weintraub [13], Khan [25] for discussions about the history of the general equilibrium theory.…”

Section: Introductionmentioning

confidence: 99%

A Direct Proof of the Gale–Nikaido–Debreu Lemma Using Sperner’s Lemma

Van

Pham³

et al. 2022

J Optim Theory Appl

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Section: Introductionmentioning

confidence: 99%

A Direct Proof of the Gale–Nikaido–Debreu Lemma Using Sperner’s Lemma

Van

Pham³

et al. 2022

J Optim Theory Appl

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“…Yet, for a number of (new) economic and game-theoretic problems these tools appeared insufficent and Ky Fan's coincidence theorem (1972), a more powerful theorem, has to be invoked; see for example Ichiishi (1983), Vohra (1991), Yang (2001), and Florenzano (2003). For many problems, one may not be contented just to know the existence of a solution, but one would like to pinpoint where a solution is located in order to evaluate and analyse the performance of the underlying model, or to appraise the effects of policy, or technical parameter changes in the model.…”

Section: Introductionmentioning

confidence: 99%

The Computation of a Coincidence of Two Mappings

Talman

Yang

2004

SSRN Journal

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Self-Consistent Transfer Operators: Invariant Measures, Convergence to Equilibrium, Linear Response and Control of the Statistical Properties

Galatolo

2022

Commun. Math. Phys.

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We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems subjected to a mean field coupling. We consider a large class of self consistent transfer operators and prove general statements about existence of invariant measures, speed of convergence to equilibrium, statistical stability and linear response. While most of the results presented in the paper are valid in a weak coupling regime, the existence results for the invariant measures we show also hold outside the weak coupling regime. We apply the general statements to examples of different nature: coupled continuous maps, coupled expanding maps, coupled systems with additive noise, systems made of different maps coupled by a mean field interaction and other examples of self consistent transfer operators not coming from coupled maps. We also consider the problem of finding the optimal coupling between maps in order to change the statistical properties of the system in a prescribed way.

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Optimality Properties of Equilibrium

Cited by 5 publications

References 0 publications

A Direct Proof of the Gale–Nikaido–Debreu Lemma Using Sperner’s Lemma

A Direct Proof of the Gale–Nikaido–Debreu Lemma Using Sperner’s Lemma

The Computation of a Coincidence of Two Mappings

Self-Consistent Transfer Operators: Invariant Measures, Convergence to Equilibrium, Linear Response and Control of the Statistical Properties

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