Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities

Ángel Arroyo, Hannes Luiro, Mikko Parviainen, Eero Ruosteenoja

Published 2018-06-28Version 1

We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in $\Omega\subset \mathbb R^n$. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in $\Omega\times \Omega$ via couplings.