State-Robust Nash Predictions In Population Games

Abstract: This paper introduces state-robust equilibrium (SRE), a local validity test for Nash predictions in finite-strategy population games when the payoff-relevant aggregate state may be misspecified. The reported prescription and payoff map are held fixed; only the state used to evaluate payoff comparisons varies. SRE is equivalent to local best-response invariance, absence of structural exposure, and validity along every vanishing interior aggregate-state error. In affine games, the tangent-cone, normal-cone, and linear-program tests characterize exposure and identify the exposing population, the pure strategy, and the aggregate-state direction. The main implication is a sharp negative result: robust mixing requires local payoff identity on the support; in generic affine games, SRE reduce to strict pure Nash equilibria, although weak boundary equilibria can survive through feasible-set protection. In affine games with polyhedral local uncertainty regions, the same inequalities yield a deterministic finite diagnostic for reported-state validity.