2019/07/22 by Marcos Antón, Fernando Charro, Antón, Marcos +3
Economics, Econometrics and Finance · Mathematics · #35B05 #35J70 #Analysis of PDEs (math.AP) #FOS: Mathematics #Game Theory and Voting Systems #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Primary 91A05 #Secondary: 65N22
paper · pdf · doi:10.48550/arxiv.1907.09219
openalex publication_date 2019/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
In this work we discuss a random Tug-of-War game in graphs where one of the players has the power to decide at each turn whether to play a round of classical random Tug-of-War, or let the other player choose the new game position in exchange of a fixed payoff. We prove that this game has a value using a discrete comparison principle and viscosity tools, as well as probabilistic arguments. This game is related to Jensen's extremal equations, which have a key role in Jensen's celebrated proof of uniqueness of infinity harmonic functions.