Application of M-Convex submodular flow problem to mathematical economics

2003 ◽  
Vol 20 (3) ◽  
pp. 257-277 ◽  
Author(s):  
Kazuo Murota ◽  
Akihisa Tamura
Keyword(s):  
Flow Problem ◽  
Mathematical Economics ◽  
Submodular Flow

scholarly journals Competitive Equilibrium and Trading Networks: A Network Flow Approach

2020 ◽  
Author(s):  
Ozan Candogan ◽  
Markos Epitropou ◽  
Rakesh V. Vohra
Keyword(s):  
Network Flow ◽  
Competitive Equilibrium ◽  
Flow Problem ◽  
Comparative Statics ◽  
Bilateral Contracts ◽  
Submodular Flow ◽  
Competitive Equilibria ◽  
Trading Networks ◽  
The Impact ◽  
Shed Light

This paper considers a network of agents who trade indivisible goods or services via bilateral contracts. Under a substitutability assumption on preferences, it is known that a competitive equilibrium exists. In “Competitive Equilibrium and Trading Networks: A Network Flow Approach,” Candogan, Epitropou, and Vohra show how to determine equilibrium outcomes as a generalized submodular flow problem. Existence of a competitive equilibrium and its equivalence to seemingly weaker notions of stability follow directly from the optimality conditions of the flow problem. The formulation enables the authors to perform comparative statics with respect to the number of buyers, sellers, and trades. In particular, they are able to shed light on the impact of new trading opportunities on the equilibrium trades, prices, and surpluses. In addition, they present algorithms for finding competitive equilibria in trading networks and testing stability.

Mathematical Economics

1983 ◽  
Author(s):  
Gerard Debreu ◽  
Werner Hildenbrand
Keyword(s):  
Mathematical Economics

Temperature field evaluation of a two-dimensional partial heat flow problem through Green's Functions

2019 ◽  
Author(s):  
Guilherme Ramalho Costa ◽  
José Aguiar santos junior ◽  
José Ricardo Ferreira Oliveira ◽  
Jefferson Gomes do Nascimento ◽  
Gilmar Guimaraes
Keyword(s):  
Temperature Field ◽  
Heat Flow ◽  
Green's Functions ◽  
Flow Problem ◽  
Green’S Functions ◽  
Field Evaluation ◽  
Two Dimensional
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