A Polynomial Time Algorithm for Computing the Arrow-Debreu Market Equilibrium for Linear Utilities
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Market equilibria for homothetic, quasi-concave utilities and economies of scale in production
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Exchange market equilibria with Leontief's utility: Freedom of pricing leads to rationality
Theoretical Computer Science
Market equilibrium via a primal--dual algorithm for a convex program
Journal of the ACM (JACM)
Settling the Complexity of Arrow-Debreu Equilibria in Markets with Additively Separable Utilities
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Spending Constraint Utilities with Applications to the Adwords Market
Mathematics of Operations Research
2-Player nash and nonsymmetric bargaining games: algorithms and structural properties
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
2-Player nash and nonsymmetric bargaining games: algorithms and structural properties
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Non-separable, quasiconcave utilities are easy in a perfect price discrimination market model
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Market equilibrium under separable, piecewise-linear, concave utilities
Journal of the ACM (JACM)
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Recent results showed PPAD-completeness of the problem of computing an equilibrium for Fisher's market model under additively separable, piecewise-linear, concave utilities. We show that introducing perfect price discrimination in this model renders its equilibrium polynomial time computable. Moreover, its set of equilibria are captured by a convex program that generalizes the classical Eisenberg-Gale program, and always admits a rational solution. We also introduce production into our model; our goal is to carve out as big a piece of the general production model as possible while still maintaining the property that a single (rational) convex program captures its equilibria, i.e., the convex program must optimize individually for each buyer and each firm.