Correspondencias e aplicações a teoria do equilibrio geral economico

Orientador: Marko Antonio Rojas MedarDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação CientificaResumo: A análise matemática apresentou, principalmente a partir da década de 60, um considerável avanço no que se refere à teoria de correspondências ou multifunções. Muitas das contribuições nesta área são devidas a economistas matemáticos, tais como Robert Aumann, Wener Wildenbrand, Gerad Debreu, dentre outros, que motivados por problemas teóricos da ciência econômica, mais especificamente à Teoria do Equilíbrio Geral e Teoria de Jogos, foram responsáveis por vários resultados que, ou generalizavam alguns fatos obtidos na análise de funções clássicas, ou mesmo apresentavam novos conceitos e resultados. O objetivo principal deste trabalho é o de, num primeiro momento, sistematizar a teoria básica de correspondências: passando por sua definição, a conceituação de convergência, o estudo da continuidade até mensurabilidade e integração. Por fim, vamos dar algumas das aplicações deste escopo à Teoria do Equilíbrio Geral com finitos bens; mais especificamente, o modelo de Equilíbrio Geral com um contínuo de agentes e puras trocas e ao modelo com produção e agentes mensuráveis, conhecido como coalition production economyAbstract: The mathematical analysis has presented, special1y after the 60's, a considerable development in what is referred to the theory of correspondences or multifunctions. Many of the contributions in this area are due to mathematic-economists, such as Robert Aumann, Wener Hildenbrand, Gerard Debreu, amongst others, that motivated by theoretical problems of economic science, more specifical1y the Theory of General Equilibrium and the Game Theory, were reponsable for many results that have, either generalized facts obtained in the analysis of c1assical functions, or even presented new concepts and results. The main goal of this work is to, in a fist stage, synthesize the basic theory of correspondences; passing by its definition, the concept of convergence, the study of continuity up to measurability and integration. In the end we give some aplications of this framework to the theory of General Equilibrium with finite goods; more specifical1y, to the model of General Equilibrium with a continuum of agents and pure exchange and the model with production and measurable agents, known as coalition production economyMestradoMestre em Matemática Aplicad

Ambiguity through confidence functions

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On the confidence preferences model

International audienceIn this paper we study the model of decision under uncertainty consistent with confidence preferences. In that model, a decision maker held beliefs represented by a fuzzy set of priors and tastes captured by a standard affine utility index on consequences. First, we find some interesting properties concerning the well-known maxmin expected utility model, taking into account the point of view of the confidence preferences model. Further, we provide new examples of preferences that capture ambiguity-averse attitudes weaker than ambiguity attitudes featured by maxmin expected utility theory. Finally, we discuss the axiomatic foundations for the confidence preferences model with optimistic behavior

Updating variational (Bewley) preferences

This paper investigates dynamically consistent updates of weighted unanimity rules given by variational Bewley preferences (VBP), a class of incomplete preferences characterized by pairs of utility index over consequences and ambiguity index over priors. We show that these dynamically consistent updates are also VBP that preserves the same ranking over consequences and feature conditional ambiguity index obtained through the full Bayesian update of the unconditional one. Moreover, we study conditional forced-choice relations, which capture choices that a decision-maker must take after learning some event. Formally, they are monotone continuous weak orders. We show that any conditional forced-choice relation that preserves the ambiguity attitude of a given unconditional VBP has a variational representation with the same affine utility function over consequences and the ambiguity index of its corresponding dynamically consistent update. Thus, our result provides a novel foundation for full Bayesian updating of variational preferences

Choquet expected discounted utility

We study intertemporal decision making under uncertainty in a purely subjective framework. The concept of stationarity, introduced by Koopmans for deterministic discounted utility, is naturally extended to a framework with uncertainty and plays a central role for both attitudes towards time and uncertainty. We show that a strong sta- tionarity axiom characterizes discounted expected utility. When considerations about correlations across time between uncertain outcomes are taken into account, a weaker stationarity axiom generalizes discounted expected utility to Choquet expected dis- counted utility, allowing for non-neutral attitudes towards subjective uncertainty

Ambiguity through confidence functions

We characterize preference relations over bounded below Anscombe and Aumann's acts and give necessary and sufficient conditions that guarantee the existence of a utility function u on consequences, a confidence function [phi] on the set of all probabilities over states of nature, and a positive threshold level of confidence [alpha]0 such that our preference relation has a functional representation J, where given an act f The level set L[alpha]0[phi]:={p:[phi](p)>=[alpha]0} reflects the priors held by the decision maker and the value [phi](p) captures the relevance of prior p for his decision. The combination of [phi] and [alpha]0 may describe the decision maker's subjective assessment of available information. An important feature of our representation is the characterization of the maximal confidence function which allows us to obtain results on comparative ambiguity aversion and on special cases, namely the subjective expected utility, the Choquet expected utility with convex capacity, and the maxmin expected utility.Confidence functions Ambiguity aversion Knightian uncertainty Ambiguity attitudes Multiple prior model