Which Nash Equilibrium? Solver-Dependent Selection on Zero-Sum Nash Polytopes

It matters because standard solvers are treated as interchangeable when selecting equilibria from the polytope of Nash equilibrium profiles that share the minimax value.

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…