Harnack's Inequality for p-Harmonic Functions via Stochastic Games

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We give a proof of asymptotic Lipschitz continuity of p-harmonious functions, that are tug-of-war game analogies of ordinary p-harmonic functions. This result is used to obtain a new proof of Lipschitz continuity and Harnack's inequality for p-harmonic functions in the case p > 2. The proof avoids classical techniques like Moser iteration, but instead relies on suitable choices of strategies for the stochastic tug-of-war game.