Alternating gradient descent energy invariants can be turned into linear equations that recover the Nash equilibrium in O(k) iterations, provided the equation system is non-degenerate.
Bailey, Gauthier Gidel, and Georgios Piliouras
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Characterizing Nash Equilibria in Zero-Sum Games: A Physics-Inspired, Parallelizable Approach with a Linear Number of Gradient Queries
Alternating gradient descent energy invariants can be turned into linear equations that recover the Nash equilibrium in O(k) iterations, provided the equation system is non-degenerate.