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Why prices need algorithms

Why prices need algorithms Why Prices Need Algorithms TIM ROUGHGARDEN and INBAL TALGAM-COHEN Stanford University Understanding when equilibria are guaranteed to exist is a central theme in economic theory, seemingly unrelated to computation. In this note we survey our main result from [Roughgarden and Talgam-Cohen 2015], which shows that the existence of pricing equilibria is inextricably connected to the computational complexity of related optimization problems: demand oracles, revenue-maximization and welfare-maximization. We demonstrate how this relationship implies, under suitable complexity assumptions, a host of impossibility results. We also suggest a complexity-theoretic explanation for the lack of useful extensions of the Walrasian equilibrium concept: such extensions seem to require the invention of novel polynomial-time algorithms for welfare-maximization. Categories and Subject Descriptors: F.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity; J.4 [Computer Applications]: Social and Behavioral Sciences-- Economics General Terms: Algorithms, Economics, Theory Additional Key Words and Phrases: Market Equilibrium, Computational Game Theory, Equilibrium Computation, Market Design, Complexity 1. INTRODUCTION Computational complexity has already had plenty to say about the computation of economic equilibria (for example, [Fischer et al. 2006; Chen et al. 2009; Chen et al. 2009; Daskalakis et al. 2009; Papadimitriou and Wilkens 2011]). The primary theme of [Roughgarden and Talgam-Cohen http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGecom Exchanges Association for Computing Machinery

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2016 by ACM Inc.
ISSN
1551-9031
DOI
10.1145/2904104.2904109
Publisher site
See Article on Publisher Site

Abstract

Why Prices Need Algorithms TIM ROUGHGARDEN and INBAL TALGAM-COHEN Stanford University Understanding when equilibria are guaranteed to exist is a central theme in economic theory, seemingly unrelated to computation. In this note we survey our main result from [Roughgarden and Talgam-Cohen 2015], which shows that the existence of pricing equilibria is inextricably connected to the computational complexity of related optimization problems: demand oracles, revenue-maximization and welfare-maximization. We demonstrate how this relationship implies, under suitable complexity assumptions, a host of impossibility results. We also suggest a complexity-theoretic explanation for the lack of useful extensions of the Walrasian equilibrium concept: such extensions seem to require the invention of novel polynomial-time algorithms for welfare-maximization. Categories and Subject Descriptors: F.2 [Theory of Computation]: Analysis of Algorithms and Problem Complexity; J.4 [Computer Applications]: Social and Behavioral Sciences-- Economics General Terms: Algorithms, Economics, Theory Additional Key Words and Phrases: Market Equilibrium, Computational Game Theory, Equilibrium Computation, Market Design, Complexity 1. INTRODUCTION Computational complexity has already had plenty to say about the computation of economic equilibria (for example, [Fischer et al. 2006; Chen et al. 2009; Chen et al. 2009; Daskalakis et al. 2009; Papadimitriou and Wilkens 2011]). The primary theme of [Roughgarden and Talgam-Cohen

Journal

ACM SIGecom ExchangesAssociation for Computing Machinery

Published: Mar 16, 2016

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