  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 in [BLO+20] to stochastic ones.
  [BLO+20] Patricia Bouyer, St\'ephane Le Roux, Youssouf Oualhadj, Mickael
Randour, and Pierre Vandenhove. Games Where You Can Play Optimally with
Arena-Independent Finite Memory. CONCUR 2020.
