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Computing Shapley's saddles

Computing Shapley's saddles Computing Shapley ™s Saddles FELIX BRANDT, MARKUS BRILL, FELIX FISCHER, PAUL HARRENSTEIN, JAN HOFFMANN Institut f r Informatik, Ludwig-Maximilians-Universit t M nchen u a u Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems; I.2.11 [Distributed Arti cial Intelligence]: Multiagent Systems; J.4 [Computer Applications]: Social and Behavioral Sciences ”Economics General Terms: Theory, Algorithms, Economics Additional Key Words and Phrases: Game Theory, Solutions Concepts, Shapley ™s Saddles, Computational Complexity 1. INTRODUCTION Game-theoretic solution concepts, such as Nash equilibrium, are playing an ever increasing role in the study of systems of autonomous agents. A common criticism of Nash equilibrium is that its existence relies on the possibility of randomizing over actions, which in many cases is deemed unsuitable, impractical, or even infeasible. In work dating back to the early 1950s Lloyd Shapley proposed ordinal set-valued solution concepts for zero-sum games that he refers to as saddles [Shapley, 1964]. Based on the elementary notions of dominance and stability, saddles are intuitively appealing, they always exist, and are unique in important classes of games. In this note, we survey recent results concerning the computational complexity of Shapley ™s saddles and identify some open problems [Brandt et 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 © 2009 by ACM Inc.
ISSN
1551-9031
DOI
10.1145/1980522.1980525
Publisher site
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Abstract

Computing Shapley ™s Saddles FELIX BRANDT, MARKUS BRILL, FELIX FISCHER, PAUL HARRENSTEIN, JAN HOFFMANN Institut f r Informatik, Ludwig-Maximilians-Universit t M nchen u a u Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems; I.2.11 [Distributed Arti cial Intelligence]: Multiagent Systems; J.4 [Computer Applications]: Social and Behavioral Sciences ”Economics General Terms: Theory, Algorithms, Economics Additional Key Words and Phrases: Game Theory, Solutions Concepts, Shapley ™s Saddles, Computational Complexity 1. INTRODUCTION Game-theoretic solution concepts, such as Nash equilibrium, are playing an ever increasing role in the study of systems of autonomous agents. A common criticism of Nash equilibrium is that its existence relies on the possibility of randomizing over actions, which in many cases is deemed unsuitable, impractical, or even infeasible. In work dating back to the early 1950s Lloyd Shapley proposed ordinal set-valued solution concepts for zero-sum games that he refers to as saddles [Shapley, 1964]. Based on the elementary notions of dominance and stability, saddles are intuitively appealing, they always exist, and are unique in important classes of games. In this note, we survey recent results concerning the computational complexity of Shapley ™s saddles and identify some open problems [Brandt et

Journal

ACM SIGecom ExchangesAssociation for Computing Machinery

Published: Dec 1, 2009

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