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Computing Good Nash Equilibria in Graphical Games

Computing Good Nash Equilibria in Graphical Games
Computing Good Nash Equilibria in Graphical Games
This paper addresses the problem of fair equilibrium selection in graphical games. Our approach is based on the data structure called the {\em best response policy}, which was proposed by Kearns et al.~\cite{kls} as a way to represent all Nash equilibria of a graphical game. In~\cite{egg}, it was shown that the best response policy has polynomial size as long as the underlying graph is a path. In this paper, we show that if the underlying graph is a bounded-degree tree and the best response policy has polynomial size then there is an efficient algorithm which constructs a Nash equilibrium that guarantees certain payoffs to all participants. Another attractive solution concept is a Nash equilibrium that maximizes the social welfare. We show that, while exactly computing the latter is infeasible (we prove that solving this problem may involve algebraic numbers of an arbitrarily high degree), there exists an FPTAS for finding such an equilibrium as long as the best response policy has polynomial size. These two algorithms can be combined to produce Nash equilibria that satisfy various fairness criteria.
Elkind, Edith
7a013473-5cd0-4e41-b907-66b30a04a400
Goldberg, Leslie Ann
3620f64c-541d-4f41-a763-e23f50acf4c3
Goldberg, Paul W.
46b110bb-a7df-406d-babc-291a17fff863
Elkind, Edith
7a013473-5cd0-4e41-b907-66b30a04a400
Goldberg, Leslie Ann
3620f64c-541d-4f41-a763-e23f50acf4c3
Goldberg, Paul W.
46b110bb-a7df-406d-babc-291a17fff863

Elkind, Edith, Goldberg, Leslie Ann and Goldberg, Paul W. (2007) Computing Good Nash Equilibria in Graphical Games. The Eighth ACM Conference on Electronic Commerce (EC'07), San Diego, CA, United States. 13 - 16 Jun 2007.

Record type: Conference or Workshop Item (Paper)

Abstract

This paper addresses the problem of fair equilibrium selection in graphical games. Our approach is based on the data structure called the {\em best response policy}, which was proposed by Kearns et al.~\cite{kls} as a way to represent all Nash equilibria of a graphical game. In~\cite{egg}, it was shown that the best response policy has polynomial size as long as the underlying graph is a path. In this paper, we show that if the underlying graph is a bounded-degree tree and the best response policy has polynomial size then there is an efficient algorithm which constructs a Nash equilibrium that guarantees certain payoffs to all participants. Another attractive solution concept is a Nash equilibrium that maximizes the social welfare. We show that, while exactly computing the latter is infeasible (we prove that solving this problem may involve algebraic numbers of an arbitrarily high degree), there exists an FPTAS for finding such an equilibrium as long as the best response policy has polynomial size. These two algorithms can be combined to produce Nash equilibria that satisfy various fairness criteria.

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More information

Published date: 2007
Additional Information: Event Dates: June 13--16, 2007
Venue - Dates: The Eighth ACM Conference on Electronic Commerce (EC'07), San Diego, CA, United States, 2007-06-13 - 2007-06-16
Organisations: Electronics & Computer Science

Identifiers

Local EPrints ID: 263821
URI: http://eprints.soton.ac.uk/id/eprint/263821
PURE UUID: 32ddcaf3-c9e3-471d-9d3b-379c41060f9d

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Date deposited: 01 Apr 2007
Last modified: 14 Mar 2024 07:38

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Contributors

Author: Edith Elkind
Author: Leslie Ann Goldberg
Author: Paul W. Goldberg

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