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Linear solvers for nonlinear games: using pivoting algorithms to find Nash equilibria in n -player games

Linear solvers for nonlinear games: using pivoting algorithms to find Nash equilibria in n... Linear Solvers for Nonlinear Games: Using Pivoting Algorithms to Find Nash Equilibria in n-Player Games JAMES R. WRIGHT and ALBERT XIN JIANG and KEVIN LEYTON-BROWN Department of Computer Science University of British Columbia Nash equilibria of two-player games are much easier to compute in practice than those of nplayer games, even though the two problems have the same asymptotic complexity. We used a recent constructive reduction to solve general games using a two-player algorithm. However, the reduction increases the game size too much to be practically usable. An open problem is to nd a more compact constructive reduction, which might make this approach feasible. Categories and Subject Descriptors: F.2.0 [Analysis of algorithms and problem complexity]: General General Terms: Algorithms, Theory, Performance, Experimentation Additional Key Words and Phrases: Nash equilibrium It is well known that nding a Nash equilibrium in a two-player game is asymptotically no easier than nding an equilibrium of an n-player game for n > 2 [Chen et al. 2009]. This is surprising, since payo €s in a two-player game are linear in the mixed strategy of the opposing player, unlike in an n-player game. Performing this computation in practice using the best known solvers, this http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM SIGecom Exchanges Association for Computing Machinery

Linear solvers for nonlinear games: using pivoting algorithms to find Nash equilibria in n -player games

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2011 by ACM Inc.
ISSN
1551-9031
DOI
10.1145/1978721.1978724
Publisher site
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Abstract

Linear Solvers for Nonlinear Games: Using Pivoting Algorithms to Find Nash Equilibria in n-Player Games JAMES R. WRIGHT and ALBERT XIN JIANG and KEVIN LEYTON-BROWN Department of Computer Science University of British Columbia Nash equilibria of two-player games are much easier to compute in practice than those of nplayer games, even though the two problems have the same asymptotic complexity. We used a recent constructive reduction to solve general games using a two-player algorithm. However, the reduction increases the game size too much to be practically usable. An open problem is to nd a more compact constructive reduction, which might make this approach feasible. Categories and Subject Descriptors: F.2.0 [Analysis of algorithms and problem complexity]: General General Terms: Algorithms, Theory, Performance, Experimentation Additional Key Words and Phrases: Nash equilibrium It is well known that nding a Nash equilibrium in a two-player game is asymptotically no easier than nding an equilibrium of an n-player game for n > 2 [Chen et al. 2009]. This is surprising, since payo €s in a two-player game are linear in the mixed strategy of the opposing player, unlike in an n-player game. Performing this computation in practice using the best known solvers, this

Journal

ACM SIGecom ExchangesAssociation for Computing Machinery

Published: Mar 1, 2011

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