The Competitive Spectral Radius of Families of Nonexpansive Mappings

The paper proves the maximin characterization (Theorem 4) and existence of a uniform value, including a stationary optimal strategy for Max, under Assumption 8; it also proves a dual minimax characterization on distance-like functions D under a uniform almost-isometry hypothesis (Theorem 5). The candidate solution correctly reproduces the maximin side and strategy arguments, but its “dual side” proof is flawed: it uses S(sup_n w_n) ≤ sup_n S(w_n), which reverses the valid inequality for this Shapley operator, and it claims the minimax characterization on D without the almost-isometry assumption that the paper explicitly requires. Hence the model overstates the result and contains a key inequality error, whereas the paper’s claims and proofs are consistent with their stated assumptions. See Theorem 4 and Theorem 5, and the continuity/compactness properties in Assumption 8 and Proposition 10 for details .