Pure Strategies in Imperfect Information Stochastic Games

Arnaud Carayol (1) , Christof Löding (2) , Olivier Serre (3)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 RWTH - Rheinisch-Westfälische Technische Hochschule Aachen University
3 IRIF (UMR_8243) - Institut de Recherche en Informatique Fondamentale

We consider imperfect information stochastic games where we require the players to use pure (i.e. non randomised) strategies. We consider reachability, safety, Büchi and co-Büchi objectives, and investigate the existence of almost-sure/positively winning strategies for the first player when the second player is perfectly informed or more informed than the first player. We obtain decidability results for positive reachability and almost-sure Büchi with optimal algorithms to decide existence of a pure winning strategy and to compute one if it exists. We complete the picture by showing that positive safety is undecidable when restricting to pure strategies even if the second player is perfectly informed.

Mots clés: Two-player imperfect information stochastic games; pure strategies; decidability/undecidability

Domaines: Informatique et théorie des jeux [cs.GT]

Arnaud Carayol, Christof Löding, Olivier Serre. Pure Strategies in Imperfect Information Stochastic Games. Fundamenta Informaticae, 2018, 160 (4), pp.361-384. ⟨10.3233/FI-2018-1687⟩. ⟨hal-01831546⟩