Equilibrium in abstract economies without ordered preferences and with a measure space of agents

1984 ◽  
Vol 13 (2) ◽  
pp. 133-142 ◽  
Author(s):  
M.Ali Khan ◽  
Rajiv Vohra
Keyword(s):  
Measure Space ◽  
Abstract Economies ◽  
Measure Space Of Agents

scholarly journals Walrasian equilibrium theory with and without free-disposal: theorems and counterexamples in an infinite-agent context

2021 ◽  
Author(s):  
Robert M. Anderson ◽  
Haosui Duanmu ◽  
M. Ali Khan ◽  
Metin Uyanik
Keyword(s):  
Recent Work ◽  
Measure Space ◽  
Equilibrium Theory ◽  
Walrasian Equilibrium ◽  
Free Disposal ◽  
Trade Offs ◽  
Finite Set ◽  
Abstract Economies ◽  
Measure Space Of Agents

AbstractThis paper provides four theorems on the existence of a free-disposal equilibrium in a Walrasian economy: the first with an arbitrary set of agents with compact consumption sets, the next highlighting the trade-offs involved in the relaxation of the compactness assumption, and the last two with a countable set of agents endowed with a weighting structure. The results generalize theorems in the antecedent literature pioneered by Shafer–Sonnenschein in 1975, and currently in the form taken in He–Yannelis 2016. The paper also provides counterexamples to the existence of non-free-disposal equilibrium in cases of both a countable set of agents and an atomless measure space of agents. One of the examples is related to one Chiaki Hara presented in 2005. The examples are of interest because they satisfy all the hypotheses of Shafer’s 1976 result on the existence of a non-free-disposal equilibrium, except for the assumption of a finite set of agents. The work builds on recent work of the authors on abstract economies, and contributes to the ongoing discussion on the modelling of “large” societies.

scholarly journals A Bayesian Abstract Economy with a Measure Space of Agents

2009 ◽  
Vol 2009 ◽  
pp. 1-11 ◽  
Author(s):  
Monica Patriche
Keyword(s):  
Asymmetric Information ◽  
Utility Function ◽  
Measure Space ◽  
Existence Results ◽  
Random Utility ◽  
Equilibrium Existence ◽  
Abstract Economy ◽  
Measure Space Of Agents

We define the model of an abstract economy with differential (asymmetric) information and a measure space of agents. We generalize N. C. Yannelis's result (2007), considering that each agent is characterised by a random preference correspondence instead of having a random utility function. We establish two different equilibrium existence results.

On the Integrability of the Ergodic Hilbert Transform for A Class of Functions with Equal Absolute Values

1998 ◽  
Vol 5 (2) ◽  
pp. 101-106
Author(s):  
L. Ephremidze
Keyword(s):  
Hilbert Transform ◽  
Measure Space ◽  
Integrable Function ◽  
Finite Measure ◽  
Ergodic Transformation ◽  
Finite Measure Space ◽  
Class Of Functions

Abstract It is proved that for an arbitrary non-atomic finite measure space with a measure-preserving ergodic transformation there exists an integrable function f such that the ergodic Hilbert transform of any function equal in absolute values to f is non-integrable.

Lacunary ideal convergence in measure for sequences of fuzzy valued functions

2021 ◽  
Vol 40 (3) ◽  
pp. 5517-5526
Author(s):  
Ömer Kişi
Keyword(s):  
Measure Space ◽  
Finite Measure ◽  
Ideal Convergence ◽  
Convergence In Measure ◽  
Ideal Form ◽  
Measurable Functions ◽  
Finite Measure Space ◽  
Convergence Of Sequences

We investigate the concepts of pointwise and uniform I θ -convergence and type of convergence lying between mentioned convergence methods, that is, equi-ideally lacunary convergence of sequences of fuzzy valued functions and acquire several results. We give the lacunary ideal form of Egorov’s theorem for sequences of fuzzy valued measurable functions defined on a finite measure space ( X , M , μ ) . We also introduce the concept of I θ -convergence in measure for sequences of fuzzy valued functions and proved some significant results.

scholarly journals Fairness and fuzzy coalitions

2021 ◽  
Author(s):  
Chiara Donnini ◽  
Marialaura Pesce
Keyword(s):  
New York ◽  
Economic Theory ◽  
Measure Space ◽  
Exchange Economy ◽  
Mathematical Methods ◽  
Competitive Equilibria ◽  
Fuzzy Coalitions ◽  
Core Allocations

AbstractIn this paper, we study the problem of a fair redistribution of resources among agents in an exchange economy á la Shitovitz (Econometrica 41:467–501, 1973), with agents’ measure space having both atoms and an atomless sector. We proceed by following the idea of Aubin (Mathematical methods of game economic theory. North-Holland, Amsterdam, New York, Oxford, 1979) to allow for partial participation of individuals in coalitions, that induces an enlargement of the set of ordinary coalitions to the so-called fuzzy or generalized coalitions. We propose a notion of fairness which, besides efficiency, imposes absence of envy towards fuzzy coalitions, and which fully characterizes competitive equilibria and Aubin-core allocations.

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