Which Nash Equilibrium? Solver-Dependent Selection on Zero-Sum Nash Polytopes
Evolving story · 1 updatesNash Equilibrium Solver Selection in Zero-Sum GamesTimeline →Research paper reveals that different Nash equilibrium solvers converge to distinct equilibria in zero-sum games, challenging the assumption of solver interchangeability.
Many two-player zero-sum games admit not a unique Nash equilibrium but a convex set of them: a polytope of profiles that all share the minimax value V* yet prescribe different behaviour. Standard solvers each converge to some equilibrium and are treated as interchangeable. We ask whether they instead select different members of the Nash set, systematically as a function of the algorithm rather than the seed. Using a tabular, exactly solvable testbed of six games with analytically known Nash sets -- including a two-dimensional Nash polytope and Kuhn poker -- we find that (i) selection is determ
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