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The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
We consider a sequential decision model over multi-tier supply chain networks and show that in particular, for series parallel networks, there is a unique equilibrium. We provide a linear time algorithm to compute the equilibrium and study…
We consider a nonlinear extension of the generalized network flow model, with the flow leaving an arc being an increasing concave function of the flow entering it, as proposed by Truemper and Shigeno. We give a polynomial time combinatorial…
Large-scale competitive market equilibrium problems arise in a wide range of important applications, including economic decision-making and intelligent manufacturing. Traditional solution methods, such as interior-point algorithms and…
We study the equilibrium computation problem for two classical resource allocation games: atomic splittable congestion games and multimarket Cournot oligopolies. For atomic splittable congestion games with singleton strategies and…
Bipartite b-matching, where agents on one side of a market are matched to one or more agents or items on the other, is a classical model that is used in myriad application areas such as healthcare, advertising, education, and general…
In this paper, inspired by the work of Megiddo on the formation of preferences and strategic analysis, we consider an early market model studied in the field of economic theory, in which each trader's utility may be influenced by the…
Market equilibria of matching markets offer an intuitive and fair solution for matching problems without money with agents who have preferences over the items. Such a matching market can be viewed as a variation of Fisher market, albeit…
We study an Arrow-Debreu economy with externalities generated by multiplex networks. Market equilibrium prices reflect both the preferences and scarcity of goods, consumers' network centralities arising from goods' externalities, as well as…
Our main contribution is a strongly polynomial algorithm for computing an equilibrium for the Arctic Auction, which is the quasi-linear extension of the linear Fisher market model. We build directly on Orlin's strongly polynomial algorithm…
This paper revisits the Arrow-Debreu general equilibrium framework through the lens of effective trade, emphasizing the distinction between theoretical and realizable market interactions. We develop the Effective Trade Model (ETM), where…
Proportional response is a well-established distributed algorithm which has been shown to converge to competitive equilibria in both Fisher and Arrow-Debreu markets, for various sub-families of homogeneous utilities, including linear and…
These notes discuss several topics in neoclassical economics and alternatives, with an aim of reviewing fundamental issues in modeling economic markets. I start with a brief, non-rigorous summary of the basic Arrow-Debreu model of general…
In this paper we studied combinatorial problems with parameterized locally budgeted uncertainty. We are looking for a solutions set such that for any parameters vector there exists a solution in the set with robustness near optimal. The…
We introduce the convex combinatorial optimization problem, a far reaching generalization of the standard linear combinatorial optimization problem. We show that it is strongly polynomial time solvable over any edge-guaranteed family, and…
As distributed energy resources (DERs) proliferate, future power system will need new market platforms enabling prosumers to trade various electricity and grid-support products. However, prosumers often exhibit complex, product…
The paper aims to find the solution of oligopoly market equilibrium problem through system of nonlinear equations. We propose modified newton method to obtain the solution of system of nonlinear equations. We show that our proposed method…
Market equilibrium is a solution concept with many applications such as digital ad markets, fair division, and resource sharing. For many classes of utility functions, equilibria can be captured by convex programs. We develop simple…
We show an auction-based algorithm to compute market equilibrium prices in a production model, where consumers purchase items under separable nonlinear utility concave functions which satisfy W.G.S(Weak Gross Substitutes); producers produce…
For a wide variety of regularization methods, algorithms computing the entire solution path have been developed recently. Solution path algorithms do not only compute the solution for one particular value of the regularization parameter but…