Finding Optimal Strategies of Almost Acyclic Simple Stochatic Games

David Auger (1) , Pierre Coucheney (2) , Yann Strozecki (2)

1 MAGMAT - Models, Algorithms, and Games for Molecules Analysis and Telecommunications
2 PRISM - Parallélisme, Réseaux, Systèmes, Modélisation

The optimal value computation for turned-based stochastic games with reachability objectives, also known as simple stochastic games, is one of the few problems in NP ∩ coNP which are not known to be in P. However, there are some cases where these games can be easily solved, as for instance when the underlying graph is acyclic. In this work, we try to extend this tractability to several classes of games that can be thought as "almost" acyclic. We give some fixed-parameter tractable or polynomial algorithms in terms of different parameters such as the number of cycles or the size of the minimal feedback vertex set.

Mots clés: algorithmic game theory; stochastic games; FPT algorithms

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

David Auger, Pierre Coucheney, Yann Strozecki. Finding Optimal Strategies of Almost Acyclic Simple Stochatic Games. 2014. ⟨hal-00941144⟩