Stochastic Games with a Single Controller and Incomplete Information

Dinah Rosenberg (1) , Eilon Solan (2) , Nicolas Vieille (1)

1 GREGH - Groupement de Recherche et d'Etudes en Gestion à HEC
2 TAU - School of Mathematical Sciences [Tel Aviv]

We study stochastic games with incomplete information on one side, in which the transition is controlled by one of the players. We prove that if the informed player also controls the transitions, the game has a value, whereas if the uninformed player controls the transitions, the max-min value as well as the min-max value exist, but they may differ. We discuss the structure of the optimal strategies, and provide extensions to the case of incomplete information on both sides.

Keywords: Minimax method; Game value; Stochastic game; Incomplete information; Optimal strategy; Uncertain system

Domains: Economy and decision science

Dinah Rosenberg, Eilon Solan, Nicolas Vieille. Stochastic Games with a Single Controller and Incomplete Information. 2002. ⟨hal-00593394⟩