1 Introduction.- 2 The linear case: random walk and harmonic functions.- 3 Tug-of-War with noise. Case p ¿ [2,8).- 4 Boundary aware tug-of-war with noise. Case p ¿ (2,8).- 5 Game-regularity and convergence. Case p ¿ (2,8).- 6 Mixed tug-of-war with noise. Case p ¿ (1,8).- A Background in probability.- B Background in Brownian motion.- C Background in PDEs. D Solutions to selected exercises.- References.- Index.

Marta Lewicka is a Polish mathematician at the University of Pittsburgh, specializing in Mathematical Analysis. Marta obtained her PhD in 2000 from Scuola Internazionale Superiore di Studi Avanzati with a thesis on Hyperbolic Systems of Conservation Laws. She has subsequently worked on Calculus of Variations, Partial Differential Equations, Continuum Mechanics, and Tug-of-War Games in relation to Nonlinear Potential Theory.