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The complexity of pure Nash equilibria

Published: 13 June 2004 Publication History

Abstract

We investigate from the computational viewpoint multi-player games that are guaranteed to have pure Nash equilibria. We focus on congestion games, and show that a pure Nash equilibrium can be computed in polynomial time in the symmetric network case, while the problem is PLS-complete in general. We discuss implications to non-atomic congestion games, and we explore the scope of the potential function method for proving existence of pure Nash equilibria.

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Cited By

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  • (2024)Equilibrium computation in multidimensional congestion gamesProceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence10.5555/3702676.3702758(1751-1779)Online publication date: 15-Jul-2024
  • (2024)Computing Nash Equilibria in Multidimensional Congestion GamesProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3663143(2309-2311)Online publication date: 6-May-2024
  • (2024)Nash Equilibria in Two-Resource Congestion Games with Player-Specific Payoff FunctionsGames10.3390/g1502000715:2(7)Online publication date: 26-Feb-2024
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William A Fahle

A relatively new research area in theoretical computer science, at the intersection of game theory and computer science, is brought to light in this paper. The problem of computing pure Nash equilibria (PNE) is discussed, and specific cases of congestion games and network congestion games are addressed. A pure Nash equilibrium is a state in a game where each player, using a pure (nonrandom) strategy, has no selfish interest in changing what she is currently doing, as it would not improve the metric. A congestion game is one where each player is competing for resources that become more costly based on how many users are using them. A network congestion game is one in which the resources are the edges of a network, and flow is sent from one node to another in the network. It is symmetric if all users send flow from the same source to the same sink. It is well known that all congestion games (unweighted) have a PNE. The main contribution of this paper is to prove that, while there is a (strongly) polynomial algorithm to find a PNE in a symmetric network congestion game, there are several other cases which are PLS-complete. The authors present an extremely complex reduction to prove the PLS-completeness of the asymmetric network congestion game in the appendix, which is most entertaining to follow. Online Computing Reviews Service

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cover image ACM Conferences
STOC '04: Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
June 2004
660 pages
ISBN:1581138520
DOI:10.1145/1007352
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 13 June 2004

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Author Tags

  1. PLS
  2. PLS-completeness
  3. complexity
  4. congestion games
  5. games
  6. local search
  7. pure Nash equilibria

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STOC04
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STOC04: Symposium of Theory of Computing 2004
June 13 - 16, 2004
IL, Chicago, USA

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Cited By

View all
  • (2024)Equilibrium computation in multidimensional congestion gamesProceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence10.5555/3702676.3702758(1751-1779)Online publication date: 15-Jul-2024
  • (2024)Computing Nash Equilibria in Multidimensional Congestion GamesProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3663143(2309-2311)Online publication date: 6-May-2024
  • (2024)Nash Equilibria in Two-Resource Congestion Games with Player-Specific Payoff FunctionsGames10.3390/g1502000715:2(7)Online publication date: 26-Feb-2024
  • (2024)A Smoothed FPTAS for Equilibria in Congestion GamesProceedings of the 25th ACM Conference on Economics and Computation10.1145/3670865.3673615(401-413)Online publication date: 8-Jul-2024
  • (2024)Separations in Proof Complexity and TFNPJournal of the ACM10.1145/366375871:4(1-45)Online publication date: 9-May-2024
  • (2024)Behind-the-Meter Load and PV Disaggregation via Deep Spatiotemporal Graph Generative Sparse Coding With Capsule NetworkIEEE Transactions on Neural Networks and Learning Systems10.1109/TNNLS.2023.328007835:10(14573-14587)Online publication date: Oct-2024
  • (2024)Joint Task Offloading and Resource Allocation in Aerial-Terrestrial UAV Networks With Edge and Fog Computing for Post-Disaster RescueIEEE Transactions on Mobile Computing10.1109/TMC.2024.335088623:9(8582-8600)Online publication date: Sep-2024
  • (2024)Methodologies for Quantifying and Optimizing the Price of AnarchyIEEE Transactions on Automatic Control10.1109/TAC.2024.340178769:11(7742-7757)Online publication date: Nov-2024
  • (2024)Mechanism Design Theory in Control Engineering: A Tutorial and Overview of Applications in Communication, Power Grid, Transportation, and Security SystemsIEEE Control Systems10.1109/MCS.2023.332991944:1(20-45)Online publication date: Feb-2024
  • (2024)The Complexity of Optimizing Atomic CongestionArtificial Intelligence10.1016/j.artint.2024.104241(104241)Online publication date: Oct-2024
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