Existence of Equilibria in Incomplete Markets with Non-Ordered Preferences

2014 ◽  
Vol 10 (03) ◽  
pp. 203-210
Author(s):  
Erkan Yalcin ◽  
Duygu Yengin
Keyword(s):  
Incomplete Markets ◽  
Competitive Equilibrium ◽  
Exchange Economy ◽  
Compact Set ◽  
Consumption Good ◽  
Linearly Independent ◽  
Finite Set ◽  
States Of Nature ◽  
Existence Of Equilibria

We consider a two-period exchange economy with a finite set of consumers, states of nature, independent assets and a single consumption good. We prove the existence of competitive equilibrium in incomplete markets, when consumption set is not assumed to be compact, set of assets is linearly independent, and individuals' preferences are not assumed to be complete or transitive. Our study therefore generalizes various results in the existing literature.

A Competitive Equilibrium Model for a Pure Exchange Economy with its Variational Formulation: A Brief Overview

2009 ◽  
Author(s):  
Carmela Vitanza ◽  
Maria Bernadette Donato ◽  
Monica Milasi ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Equilibrium Model ◽  
Variational Formulation ◽  
Competitive Equilibrium ◽  
Exchange Economy ◽  
Pure Exchange ◽  
Pure Exchange Economy

scholarly journals Existence of Equilibria and Fixed Points of Set-Valued Mappings on Epi-Lipschitz Sets with Weak Tangential Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-9
Author(s):  
Messaoud Bounkhel
Keyword(s):  
Fixed Points ◽  
Tangent Cone ◽  
Compact Set ◽  
Set Valued Mapping ◽  
Clarke Tangent Cone ◽  
Set Valued Mappings ◽  
Existence Of Equilibria

We prove a new result of existence of equilibria for an u.s.c. set-valued mappingFon a compact setSofRnwhich is epi-Lipschitz and satisfies a weak tangential condition. Equivalently this provides existence of fixed points of the set-valued mappingx⇉F(x)-x. The main point of our result lies in the fact that we do not impose the usual tangential condition in terms of the Clarke tangent cone. Illustrative examples are stated showing the importance of our results and that the existence of such equilibria does not need necessarily such usual tangential condition.

New proposals for modelling and solving the problem of covering solids using spheres of different radii

2020 ◽  
Vol 54 (3) ◽  
pp. 873-882
Author(s):  
Pedro Henrique González Silva ◽  
Ana Flávia U. S. Macambira ◽  
Renan Vicente Pinto ◽  
Luidi Simonetti ◽  
Nelson Maculan ◽  
...  
Keyword(s):  
Data Mining ◽  
Convex Optimization ◽  
Objective Function ◽  
Hybrid Method ◽  
Optimization Problem ◽  
Compact Set ◽  
Computational Results ◽  
Quadratic Constraints ◽  
Convex Optimization Problem ◽  
Finite Set

Given a solid T, represented by a compact set in ℝ3, the aim of this work is to find a covering of T by a finite set of spheres of different radii. Some level of intersection between the spheres is necessary to cover the solid. Moreover, the volume occupied by the spheres on the outside of T is limited. This problem has an application in the planning of a radio-surgery treatment known by Gamma Knife and can be formulated as a non-convex optimization problem with quadratic constraints and linear objective function. In this work, two new linear mathematical formulations with binary variables and a hybrid method are proposed. The hybrid method combines heuristic, data mining and an exact method. Computational results show that the proposed methods outperform the ones presented in the literature.

scholarly journals Competitive Equilibrium with Indivisible Goods and Generic Budgets

2021 ◽  
Vol 46 (1) ◽  
pp. 382-403
Author(s):  
Moshe Babaioff ◽  
Noam Nisan ◽  
Inbal Talgam-Cohen
Keyword(s):  
Competitive Equilibrium ◽  
Future Research ◽  
Random Perturbations ◽  
Equilibrium Existence ◽  
Demand And Supply ◽  
Single Item ◽  
Small Random Perturbations ◽  
Classic Solution ◽  
Existence Of Equilibria ◽  
Artificial Currency

Competitive equilibrium from equal incomes (CEEI) is a classic solution to the problem of fair and efficient allocation of goods (Foley 1967, Varian 1974). Every agent receives an equal budget of artificial currency with which to purchase goods, and prices match demand and supply. However, a CEEI is not guaranteed to exist when the goods are indivisible even in the simple two-agent, single-item market. Yet it is easy to see that, once the two budgets are slightly perturbed (made generic), a competitive equilibrium does exist. In this paper, we aim to extend this approach beyond the single-item case and study the existence of equilibria in markets with two agents and additive preferences over multiple items. We show that, for agents with equal budgets, making the budgets generic—by adding vanishingly small random perturbations—ensures the existence of equilibrium. We further consider agents with arbitrary nonequal budgets, representing nonequal entitlements for goods. We show that competitive equilibrium guarantees a new notion of fairness among nonequal agents and that it exists in cases of interest (such as when the agents have identical preferences) if budgets are perturbed. Our results open opportunities for future research on generic equilibrium existence and fair treatment of nonequals.

scholarly journals Equilibrium in a Reinsurance Syndicate; Existence, Uniqueness and Characterization

1993 ◽  
Vol 23 (2) ◽  
pp. 185-211 ◽  
Author(s):  
Knut K. Aase
Keyword(s):  
Competitive Equilibrium ◽  
Sufficient Conditions ◽  
Exchange Economy ◽  
Exchange Equilibrium ◽  
Optimal Contracts ◽  
Pure Exchange ◽  
Pure Exchange Economy ◽  
The One ◽  
Uniqueness Of Equilibrium ◽  
Reinsurance Market

AbstractThis paper attempts to give an overview of the pricing of risks in a pure exchange economy, where trade takes place at time zero and where uncertainty is revealed at time one. An economic equilibrium model under uncertainty is formulated, where conditions characterizing a Pareto optimal exchange equilibrium are derived. We present two sets of sufficient conditions for the existence of an equilibrium, and demonstrate how equilibria can be characterized through several examples. Uniqueness of equilibrium is also discussed. Special attention is given to the principal components that the premiums in a reinsurance market must depend upon. We also apply the general theory to the risk exchange problem between a policyholder and an insurer, and in particular we compute market premiums of the resulting optimal contracts.It is emphasized throughout how the formulation of a competitive equilibrium, rather than merely a general risk exchange formulation, is of particular interest in deriving a well-defined and unique set of equilibrium premiums in an insurance market. The theory is put into a framework which is fruitful for extensions beyond the one-period case.

The Invisible Hand

2018 ◽  
Author(s):  
Robert Sugden
Keyword(s):  
Competitive Equilibrium ◽  
Exchange Economy ◽  
Invisible Hand ◽  
The Core ◽  
Pareto Efficient ◽  
New Formulation ◽  
Over Time ◽  
The Invisible

Chapter 6 presents a new formulation of Adam Smith’s ‘invisible hand’ argument. The underlying idea is that markets are valuable because they provide opportunities for voluntary transactions (rather than because they satisfy preferences). I propose a ‘Strong Interactive Opportunity Criterion’ which requires that all opportunities for feasible and non-dominated transactions within groups of individuals are made available to those individuals. I define competitive equilibrium without making assumptions about the rationality of individuals’ choices and show that the Strong Interactive Opportunity Criterion is satisfied in every competitive equilibrium of an exchange economy. This result is analogous with the classic theorems that every competitive equilibrium is Pareto-efficient and is in the ‘core’ of the economy. I extend these results to ‘storage economies’ in which trade and consumption take place over time and in which individuals’ choices may be dynamically inconsistent.

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