On total functions, existence theorems and computational complexity
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Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
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The spending constraint model for market equilibrium: algorithmic, existence and uniqueness results
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Market equilibrium via a primal--dual algorithm for a convex program
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Continuity Properties of Equilibria in Some Fisher and Arrow-Debreu Market Models
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Extending polynomial time computability to markets with demand correspondences
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A perfect price discrimination market model with production, and a (rational) convex program for it
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2-Player nash and nonsymmetric bargaining games: algorithms and structural properties
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Non-separable, quasiconcave utilities are easy in a perfect price discrimination market model
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Distributed algorithms via gradient descent for fisher markets
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A Perfect Price Discrimination Market Model with Production, and a Rational Convex Program for It
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The notion of a rational convex program, and an algorithm for the Arrow-Debreu Nash bargaining game
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The notion of a rational convex program, and an algorithm for the arrow-debreu Nash bargaining game
Journal of the ACM (JACM)
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Tatonnement in ongoing markets of complementary goods
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The complexity of non-monotone markets
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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The notion of a “market” has undergone a paradigm shift with the Internet. Totally new and highly successful markets have been defined and launched by Internet companies, which already form an important part of today's economy and are projected to grow considerably in the future. Another major change is the availability of massive computational power for running these markets in a centralized or distributed manner. In view of these new realities, the study of market equilibria, an important, though essentially nonalgorithmic, theory within mathematical economics, needs to be revived and rejuvenated via an inherently algorithmic approach. Such a theory should not only address traditional market models, but also define new models for some of the new markets. We present a new, natural class of utility functions that allow buyers to explicitly provide information on their relative preferences as a function of the amount of money spent on each good. These utility functions offer considerable expressivity, especially in Google's Adwords market. In addition, they lend themselves to efficient computation, while retaining some of the nice properties of traditional models. The latter include weak gross substitutability, and the uniqueness and continuity of equilibrium prices and utilities.