On the existence and uniqueness of p-harmonious functions
  We give a self-contained and short proof for the existence, uniqueness and measurability of so called $p$-harmonious functions. The proofs only use elementary analytic tools. As a consequence, we obtain existence, uniqueness and measurability of value functions for the tug-of-war game with noise. 
Hannes Luiro, Mikko Parviainen, and Eero Saksman
math.AP