Problem
Research questions and friction points this paper is trying to address.
Nash Equilibrium
Network Congestion Games
Network Coordination Games
Computational Complexity
CLS-complete
The Complexity of Nash Equilibrium in Network Congestion and Coordination Games
🤖 AI Summary
This study addresses the long-standing absence of precise complexity characterizations for computing Nash equilibria in network congestion games and coordination games. By leveraging the Continuous Local Search (CLS) complexity framework alongside multilinear algebraic analysis techniques, this work rigorously establishes that computing Nash equilibria for these games, as well as finding Karush–Kuhn–Tucker (KKT) points of bilinear polynomials, are CLS-complete problems. This research provides the first proof of CLS-completeness for equilibrium computation in such game-theoretic settings, thereby determining strict complexity lower bounds for the associated problems. These findings significantly extend the complexity boundaries of algorithmic game theory and strengthen the theoretical foundations of combinatorial optimization.
📝 Abstract
We show that computing a Nash equilibrium is CLS-complete for linear network congestion and network coordination games. As a result, finding a KKT point of a bilinear polynomial is CLS-complete.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Nash Equilibrium
CLS-complete
Network Congestion Games
Network Coordination Games
KKT point
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