Title :
Concave Generalized Flows with Applications to Market Equilibria
Author_Institution :
Dept. of Manage., London Sch. of Econ., London, UK
Abstract :
We consider a nonlinear extension of the generalized network How model, with the How leaving an arc being an increasing concave function of the How entering it, as proposed by Truemper [1] and Shigeno [2]. We give a polynomial time combinatorial algorithm for solving corresponding How maximization problems, finding an ε-approximate solution in O(m(m + log n) log(MUm/ε)) arithmetic operations and value oracle queries, where M and U are upper bounds on simple parameters. This also gives a new algorithm for linear generalized Hows, an efficient, purely scaling variant of the Fat-Path algorithm by Goldberg, Plotkin and Tardos [3], not using any cycle cancellations. We show that this general convex programming model serves as a common framework for several market equilibrium problems, including the linear Fisher market model and its various extensions. Our result immediately provides combinatorial algorithms for various extensions of these market models. This includes nonsymmetric Arrow-Debreu Nash bargaining, settling an open question by Vazirani [4].
Keywords :
combinatorial mathematics; computational complexity; convex programming; game theory; stock markets; How maximization problems; approximate solution; arithmetic operations; concave function; concave generalized flows; fat-path algorithm; general convex programming model; generalized network How model; linear Fisher market model; market equilibria; nonsymmetric Arrow-Debreu Nash bargaining; polynomial time combinatorial algorithm; value oracle queries; Approximation algorithms; Complexity theory; Educational institutions; Linear approximation; Polynomials; Transportation; convex programming; generalized flows; market equilibrium; network flow algorithms;
Conference_Titel :
Foundations of Computer Science (FOCS), 2012 IEEE 53rd Annual Symposium on
Conference_Location :
New Brunswick, NJ
Print_ISBN :
978-1-4673-4383-1
DOI :
10.1109/FOCS.2012.33