A Course on Tug-of-War Games with Random Noise

Introduction and Basic Constructions

  • Marta Lewicka

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Marta Lewicka
    Pages 1-7
  3. Back Matter
    Pages 163-254

About this book


This graduate textbook provides a detailed introduction to the probabilistic interpretation of nonlinear potential theory, relying on the recently introduced notion of tug-of-war games with noise.

The book explores both basic and more advanced constructions, carefully explaining the parallel between linear and nonlinear cases. The presentation is self-contained with many exercises, making the book suitable as a textbook for a graduate course, as well as for self-study. Extensive background and auxiliary material allow the tailoring of courses to individual student levels.


Tug-of-War games nonlinear potential theory game theory p-Laplacian discrete stochastic processes games with noise mean value properties regularity theory

Authors and affiliations

  • Marta Lewicka
    • 1
  1. 1.Department of MathematicsUniversity of PittsburghPittsburghUSA

Bibliographic information