scholarly journals An Equilibrium Model of Interbank Networks Based on Variational Inequalities

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Shouwei Li ◽  
Jianmin He
Keyword(s):  
Variational Inequality ◽  
Equilibrium Model ◽  
Existence And Uniqueness ◽  
Decision Makers ◽  
Interbank Market ◽  
Qualitative Properties ◽  
Equilibrium Conditions ◽  
Trust Network ◽  
Credit Network ◽  
Equilibrium Pattern

We develop an equilibrium model of credit network and trust network in the interbank market. We consider two kinds of decision makers including banks with liquidity surplus and banks with liquidity shortage. We model the behavior of the decision makers, derive the equilibrium conditions, and establish the variational inequality formulation for interbank credit network and trust network. We then utilize the variational inequality formulation to obtain qualitative properties of the equilibrium pattern in terms of existence and uniqueness.

Closed-loop supply chain network equilibrium model and its Newton method

Kybernetes ◽  
2016 ◽  
Vol 45 (3) ◽  
pp. 393-410 ◽  
Author(s):  
Hongru Xu ◽  
Erbao Cao
Keyword(s):  
Supply Chain ◽  
Variational Inequality ◽  
Newton Method ◽  
Equilibrium Model ◽  
Equilibrium Solution ◽  
Closed Loop ◽  
Network Equilibrium ◽  
Equilibrium Conditions ◽  
Content Type ◽  
Proposed Model

Purpose – The purpose of this paper is to develop a closed-loop supply chain (CLSC) network equilibrium model which consists of manufactures, retailers and consumer markets engaged in a Cournot pricing game with heterogeneous multi-product. Design/methodology/approach – The authors model the optimal behavior of the various decision makers and CLSC network equilibrium, and derive the equilibrium conditions based on variational inequality approach. The authors present a new Newton method to solve the proposed model. Findings – The authors find that the algorithm converges to the solution rapidly for most cases. Besides, the authors discuss the effect of some parameters on the equilibrium solution of the model, and give some insights for policy makers, such as improving the technology level of the manufacturer, reducing the cost of waste disposal and increase the minimum ration of used product to total quantity. Originality/value – The authors derive the network equilibrium conditions by the variational inequality formulation in order to obtain the computation of the equilibrium flows and prices. The authors present a new Newton method to solve the proposed model. The authors discuss the effect of some parameters on the equilibrium solution of the model, and give some managerial insights

Super Efficiency of Multicriterion Network Equilibrium Model and Vector Variational Inequality

2011 ◽  
Vol 153 (2) ◽  
pp. 485-496 ◽  
Author(s):  
Yunan Wu ◽  
Yuchen Peng ◽  
Long Peng ◽  
Ling Xu
Keyword(s):  
Variational Inequality ◽  
Equilibrium Model ◽  
Vector Variational Inequality ◽  
Network Equilibrium ◽  
Super Efficiency

Existence and uniqueness of solutions of the generalized polynomial variational inequality

2019 ◽  
Vol 14 (6) ◽  
pp. 1571-1582 ◽  
Author(s):  
Jing Wang ◽  
Zheng-Hai Huang ◽  
Yang Xu
Keyword(s):  
Variational Inequality ◽  
Existence And Uniqueness ◽  
Uniqueness Of Solutions ◽  
Generalized Polynomial

A Nonlinear Equation Framework for Solving Network Equilibrium Problems

1984 ◽  
Vol 16 (1) ◽  
pp. 67-80 ◽  
Author(s):  
C Fisk
Keyword(s):  
Existence And Uniqueness ◽  
Equilibrium Problems ◽  
Iterative Solution ◽  
System Of Nonlinear Equations ◽  
Network Equilibrium ◽  
Convergence Properties ◽  
Equilibrium Conditions ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Network Equilibrium Problems

The author presents a general framework for formulating network equilibrium problems in which the equilibrium conditions are given by a system of nonlinear equations. Existence and uniqueness results are presented, and iterative solution techniques with well-defined convergence properties are suggested. For illustrative purposes, these techniques are applied to a specific two-mode equilibrium model; a discussion comparing some aspects of this approach with other existing approaches is included.

Existence and Uniqueness Properties of an Asymmetric Two-Mode Equilibrium Model

1981 ◽  
Vol 15 (4) ◽  
pp. 318-328 ◽  
Author(s):  
Caroline Fisk ◽  
Sang Nguyen
Keyword(s):  
Equilibrium Model ◽  
Existence And Uniqueness

Optimization of Port Supply Chain Super Network under Electronic Commerce

2012 ◽  
Vol 605-607 ◽  
pp. 557-561
Author(s):  
Hai Yan Xie ◽  
Xiao Liu ◽  
De Peng Zhao
Keyword(s):  
Supply Chain ◽  
Variational Inequalities ◽  
Electronic Commerce ◽  
Network Model ◽  
Decision Makers ◽  
Projection Algorithm ◽  
Decision Criteria ◽  
Equilibrium Conditions

This paper establishes a three-layer port supply chain super network model for multiple decision criteria which consists of M suppliers, N port agents and K customers. The establishment of the model is based on the principles of competition in the same layer and cooperation between different layers. Then, from the perspective of suppliers, port agents and customers, we respectively model the optimizing behavior of the various decision makers by using variational inequalities, and we derive the equilibrium conditions of the entire supply chain by using improved projection algorithm. Finally, we prove the feasibility of the model by experiment.

scholarly journals On the Theory of ψ-Hilfer Nonlocal Cauchy Problem

2021 ◽  
pp. 161-177
Author(s):  
Mohammed A. Almalahi ◽  
Satish K. Panchal
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Fixed Point ◽  
Constant Coefficient ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Representation Formula ◽  
Qualitative Properties ◽  
Fractional Differential ◽  
Nonlocal Cauchy Problem

In this paper, we derive the representation formula of the solution for ψ-Hilfer fractional differential equation with constant coefficient in the form of Mittag-Leffler function by using Picard’s successive approximation. Moreover, by using some properties of Mittag-Leffler function and fixed point theorems such as Banach and Schaefer, we introduce new results of some qualitative properties of solution such as existence and uniqueness. The generalized Gronwall inequality lemma is used in analyze Eα -Ulam-Hyers stability. Finally, one example to illustrate the obtained results

scholarly journals Analysis of Ode Models for Malaria Propagation

2020 ◽  
Vol 17 (1) ◽  
pp. 31-39
Author(s):  
Fanni Dorner ◽  
Rahele Mosleh
Keyword(s):  
Existence And Uniqueness ◽  
Numerical Models ◽  
Equilibrium Points ◽  
Epidemiological Models ◽  
Qualitative Properties ◽  
Data Set ◽  
Ode Models ◽  
Population Dynamics Models ◽  
Dynamics Models ◽  
Uniqueness Of Equilibrium

AbstractEpidemiological models play an important role in the study of diseases. These models belong to population dynamics models and can be characterized with differential equations. In this paper we focus our attention on two epidemic models for malaria spreading, namely Ross-, and extended Ross model. As both the continous and the corresponding numerical models should preserve the basic qualitative properties of the phenomenon, we paid special attention to its examination, and proved their invariance with reference to the data set. Moreover, existence and uniqueness of equilibrium points for both models of malaria are considered. We demonstrate the theoritical results with numerical simulations.

Building models of learning and the equilibrium process

2017 ◽  
Author(s):  
Lawrence A. Boland
Keyword(s):  
Equilibrium Model ◽  
Inductive Learning ◽  
Methodological Individualism ◽  
Decision Makers ◽  
Learning Needs ◽  
Realistic Theory ◽  
Building Models ◽  
Equilibrium Process ◽  
Equilibrium Economic ◽  
Almost All

This chapter reconsiders the two contrary views of knowledge and hence of learning that was discussed in Chapter 6. One is the quantity-based view, which plays a role whenever model builders appeal to some form of inductive learning, and a quality-based view, which is the view promoted by Plato’s early Socrates but rarely recognized by equilibrium model builders. Whichever view is adopted, learning needs to be addressed when recognizing any role for knowledge in equilibrium economic models. In this regard, the chapter addresses the main limitation of almost all equilibrium models—namely, the failure to incorporate a realistic theory of the decision makers’ knowledge and learning in the model. The chapter ends by showing how methodological individualism can be generalized. And if it is, it can thereby serve as a basis for a more realistic explanation of an equilibrium’s stability.

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