The Lipschitz Constant of Perturbed Anonymous Games

Ron Peretz, Amnon Schreiber

The worst-case Lipschitz constant of an $n$-player $k$-action $\delta$-perturbed game, $\lambda(n,k,\delta)$, is characterised. In the case of $k\geq 3$, $\lambda(n,k,\delta)$ is identified with the passage probability of a certain symmetric random walk on $\mathbb Z$. The other case, $k=2$, is estimated asymptotically, while it is conjectured to equal the probability that two i.i.d.\ Binomial random variables are equal.

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