Steering Equilibrium Selection in Regularized Self-Play via the Reference Policy

Regularized self-play -- the family behind DeepNash's Stratego play -- drives a two-player zero-sum policy to a Nash equilibrium by best-responding to a slowly moving, entropy-regularized reference policy $ρ$. When the game has a polytope of value-equivalent equilibria, the regularizer silently breaks the tie: with a uniform reference it selects the maximum-entropy member, the I-projection of $ρ$ onto the Nash set. Can the reference be used to choose the equilibrium on purpose? On five exactly solvable games plus a 2-D polytope, with exact best responses and equivalence tests over independent seeds, anchoring the reference at a target member and refining steers self-play to that member wi...

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