2024/09/08 by Adjei, Axel, Krishnan, Neil, Mossel, Elchanan
Decision Sciences · Mathematics · Physics and Astronomy · #Combinatorics (math.CO) #Complex Network Analysis Techniques #FOS: Mathematics #Game Theory and Applications #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2409.05201
openalex publication_date 2024/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A recent paper by Bhatia, Chin, Mani, and Mossel (2026) defined stochastic processes modeling the game of War for \em two players with n cards. That paper showed that these models, assuming uniform random decks, are equivalent to the Gambler's Ruin problem and therefore have an expected termination time of Θ(n2). In this paper, we generalize these models to \em any number of players m. We prove that the game with m players is equivalent to a simple sticky random walk on an (m-1)-simplex; therefore, the termination time is the same as the absorption time of the simple sticky random walk. Unlike Gambler's Ruin, this absorption time has not been analyzed before. We show that the absorption time of the walk and the termination time of the game are both Θ(n2) for any number of players.