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Equilibrium computation in multidimensional congestion games: CSP and learning dynamics approaches

Published: 15 July 2024 Publication History

Abstract

We present algorithms of two flavors—one rooted in constraint satisfaction problems (CSPs) and the other in learning dynamics—to compute pure-strategy Nash equilibrium (PSNE) in k-dimensional congestion games (k-DCGs) and their variants. The two algorithmic approaches are driven by whether or not a PSNE is guaranteed to exist. We first show that deciding the existence of a PSNE in a k-DCG is NP-complete even when players have binary and unit demand vectors. For general cost functions (potentially non-monotonic), we devise a new CSP-inspired algorithmic framework for PSNE computation, leading to algorithms that run in polynomial time under certain assumptions while offering exponential savings over standard CSP algorithms. We further refine these algorithms for variants of k-DCGs. Our experiments demonstrate the effectiveness of this new CSP framework for hard, non-monotonic k-DCGs. We then provide learning dynamics-based PSNE computation algorithms for linear and exponential cost functions. These algorithms run in polynomial time under certain assumptions. For general cost, we give a learning dynamics algorithm for an (α, β)-approximate PSNE (for certain α and β). Lastly, we also devise polynomial-time algorithms for structured demands and cost functions.

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cover image Guide Proceedings
UAI '24: Proceedings of the Fortieth Conference on Uncertainty in Artificial Intelligence
July 2024
4270 pages
  • Editors:
  • Negar Kiyavash,
  • Joris M. Mooij

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  • Google
  • DEShaw&Co
  • Barcelona School of Economics
  • Universitat Pompeu Fabra

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Published: 15 July 2024

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