Equilibrium Computation in Multidimensional Congestion Games: CSP and Learning Dynamics Approaches

Mohammad T. Irfan, Hau Chan, Jared Soundy

Keywords: computational game theory, congestion game, constraint satisfaction problem, CSP, learning dynamics, Nash equilibrium

TL;DR: Presents two algorithmic approaches for computing equilibria in multidimensional congestion games, driven by whether or not an equilibrium is guaranteed to exist.

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.

List Of Authors: Irfan, Mohammad T and Chan, Hau and Soundy, Jared

Submission Number: 503