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.

Equilibrium theory with a measure space of possibly satiated consumers

2003 ◽  
Vol 39 (3-4) ◽  
pp. 175-196 ◽  
Author(s):  
Bernard Cornet ◽  
Mihaela Topuzu ◽  
Ayşegül Yildiz
Keyword(s):  
Measure Space ◽  
Equilibrium Theory

Weighted Fuzzy Averages in Fuzzy Environment: Part II. Generalized Weighted Fuzzy Expected Values in Fuzzy Environment

2003 ◽  
Vol 11 (02) ◽  
pp. 159-172 ◽  
Author(s):  
G. Sirbiladze ◽  
A. Sikharulidze
Keyword(s):  
Measure Space ◽  
Expected Value ◽  
Fuzzy Measure ◽  
Weighted Averages ◽  
Fuzzy Environment ◽  
Fuzzy Expected Value ◽  
Interval Extension ◽  
Finite Set ◽  
Expected Values ◽  
Iteration Processes

The weighted fuzzy expected value (WFEV) of the population for a sampling distribution was introduced in 1. In 2 the notion of WFEV is generalized for any fuzzy measure on a finite set (WFEVg). The latter paper also describes the notions of weighted fuzzy expected intervals WFEI and WFEIg which are an interval extension of WFEV and WFEVg, respectively, when due to ''scarce'' data the fuzzy expected value (FEV) 3 does not exist, but the fuzzy expected interval (FEI) 3 does. In this paper, The generalizations GWFEVg and GWFEIg of WFEVg and WFEIg, respectively, are introduced for any fuzzy measure space. Furthermore, the generalized weighted fuzzy expected value is expressed in terms of two monotone expectation (ME)4 values with respect to the Lebesgue measure on [0,1]. The convergence of iteration processes is provided by an appropriate choice of a ''weight'' function. In the interval extension (GWFEIg) the so-called combinatorial interval extension of a function 5 is successfully used, which is clearly illustrated by examples. Several examples of the use of the new weighted averages are discussed. In many cases these averages give better estimations than classical estimators of central tendencies such as mean, median or the fuzzy ''classical'' estimators FEV, FEI and ME.

Synthesis of Watt-type Timed Curve Generators and Selection from Continuous Cognate Spaces

2021 ◽  
pp. 1-11
Author(s):  
Aravind Baskar ◽  
Mark Plecnik
Keyword(s):  
Recent Work ◽  
Polynomial Systems ◽  
Number Of Solutions ◽  
End Effector ◽  
Continuous Space ◽  
Trade Offs ◽  
Synthesis Of Mechanisms ◽  
Free Parameters ◽  
Selection Of

Abstract Following recent work on Stephenson-type mechanisms, the synthesis equations of Watt six-bar mechanisms that act as timed curve generators are formulated and systematically solved. Four variations of the problem arise by assigning the actuator and end effector onto different links. The approach produces exact synthesis of mechanisms up to eight precision points. Polynomial systems are formulated and their maximum number of solutions is estimated using the algorithm of random monodromy loops. Certain variations of Watt timed curve generators possess free parameters that do not affect the output motion, indicating a continuous space of cognate mechanisms. Packaging compactness, clearance, and dimensional sensitivity are characterized across the cognate space to illustrate trade-offs and aid in selection of a final mechanism.

scholarly journals Plünnecke inequalities for measure graphs with applications

2015 ◽  
Vol 37 (2) ◽  
pp. 418-439
Author(s):  
KAMIL BULINSKI ◽  
ALEXANDER FISH
Keyword(s):  
Recent Work ◽  
Measure Space ◽  
Correspondence Principle ◽  
Abelian Groups ◽  
Density Estimates ◽  
Vertex Set ◽  
Banach Density ◽  
Measure Preserving Actions

We generalize Petridis’s new proof of Plünnecke’s graph inequality to graphs whose vertex set is a measure space. Consequently, by a recent work of Björklund and Fish, this gives new Plünnecke inequalities for measure-preserving actions which enable us to deduce, via a Furstenberg correspondence principle, Banach density estimates in countable abelian groups that extend those given by Jin.

Number of variables is equivalent to space

2001 ◽  
Vol 66 (3) ◽  
pp. 1217-1230 ◽  
Author(s):  
Neil Immerman ◽  
Jonathan F. Buss ◽  
David A. Mix Barrington
Keyword(s):  
Turing Machine ◽  
Descriptive Complexity ◽  
First Order ◽  
Trade Offs ◽  
Finite Set ◽  
The Universe

AbstractWe prove that the set of properties describable by a uniform sequence of first-order sentences using at most k + 1 distinct variables is exactly equal to the set of properties checkable by a Turing machine in DSPACE[nk] (where n is the size of the universe). This set is also equal to the set of properties describable using an iterative definition for a finite set of relations of arity k. This is a refinement of the theorem PSPACE = VAR[O[1]] [8]. We suggest some directions for exploiting this result to derive trade-offs between the number of variables and the quantifier depth in descriptive complexity.

scholarly journals UNDECIDABILITY AND THE DEVELOPABILITY OF PERMUTOIDS AND RIGID PSEUDOGROUPS

2017 ◽  
Vol 5 ◽  
Author(s):  
MARTIN R. BRIDSON ◽  
HENRY WILTON
Keyword(s):  
Recent Work ◽  
Permutation Group ◽  
Inverse Semigroups ◽  
Existence Problem ◽  
Finitely Presented Groups ◽  
Finite Permutation Group ◽  
Finite Set ◽  
Finitely Presented

A permutoid is a set of partial permutations that contains the identity and is such that partial compositions, when defined, have at most one extension in the set. In 2004 Peter Cameron conjectured that there can exist no algorithm that determines whether or not a permutoid based on a finite set can be completed to a finite permutation group. In this note we prove Cameron’s conjecture by relating it to our recent work on the profinite triviality problem for finitely presented groups. We also prove that the existence problem for finite developments of rigid pseudogroups is unsolvable. In an appendix, Steinberg recasts these results in terms of inverse semigroups.

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