Patricia Bouyer ; Youssouf Oualhadj ; Mickael Randour ; Pierre Vandenhove - Arena-Independent Finite-Memory Determinacy in Stochastic Games

lmcs:9201 - Logical Methods in Computer Science, December 1, 2023, Volume 19, Issue 4 - https://doi.org/10.46298/lmcs-19(4:18)2023
Arena-Independent Finite-Memory Determinacy in Stochastic GamesPreprint

Authors: Patricia Bouyer ; Youssouf Oualhadj ; Mickael Randour ; Pierre Vandenhove

    We study stochastic zero-sum games on graphs, which are prevalent tools to model decision-making in presence of an antagonistic opponent in a random environment. In this setting, an important question is the one of strategy complexity: what kinds of strategies are sufficient or required to play optimally (e.g., randomization or memory requirements)? Our contributions further the understanding of arena-independent finite-memory (AIFM) determinacy, i.e., the study of objectives for which memory is needed, but in a way that only depends on limited parameters of the game graphs. First, we show that objectives for which pure AIFM strategies suffice to play optimally also admit pure AIFM subgame perfect strategies. Second, we show that we can reduce the study of objectives for which pure AIFM strategies suffice in two-player stochastic games to the easier study of one-player stochastic games (i.e., Markov decision processes). Third, we characterize the sufficiency of AIFM strategies through two intuitive properties of objectives. This work extends a line of research started on deterministic games to stochastic ones.


    Volume: Volume 19, Issue 4
    Published on: December 1, 2023
    Accepted on: August 23, 2023
    Submitted on: March 11, 2022
    Keywords: Computer Science - Computer Science and Game Theory,Computer Science - Formal Languages and Automata Theory,Computer Science - Logic in Computer Science

    Consultation statistics

    This page has been seen 507 times.
    This article's PDF has been downloaded 130 times.