The Lipschitz Constant of Perturbed Anonymous Games
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The worst-case Lipschitz constant of an n-player k-action δ-perturbed game, λ(n,k,δ), is given an explicit probabilistic description. In the case of k≥ 3, λ(n,k,δ) is identified with the passage probability of a certain symmetric random walk on ℤ. In the case of k=2 and n even, λ(n,2,δ) is identified with the probability that two two i.i.d. Binomial random variables are equal. The remaining case, k=2 and n odd, is bounded through the adjacent (even) values of n. Our characterisation implies a sharp closed form asymptotic estimate of λ(n,k,δ) as δ n /k→∞.
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