On the values of repeated games with signals

Hugo Gimbert (1) , Jérôme Renault (2) , Sylvain Sorin (3) , Xavier Venel (4, 5) , Wieslaw Zielonka (6)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique
2 GREMAQ - Groupe de recherche en économie mathématique et quantitative
3 IMJ - Institut de Mathématiques de Jussieu
4 CES - Centre d'économie de la Sorbonne
5 PSE - Paris School of Economics
6 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

We study the existence of different notions of values in two-person zero-sum repeated games where the state evolves and players receive signals. We provide some examples showing that the limsup value and the uniform value may not exist in general. Then, we show the existence of the value for any Borel payoff function if the players observe a public signal including the actions played. We prove also two other positive results without assumptions on the signaling structure: the existence of the $\sup$-value and the existence of the uniform value in recursive games with non-negative payoffs.

Mots clés: Borel evaluation; Repeated Games with signals

Domaines: Optimisation et contrôle [math.OC]; Economies et finances

Hugo Gimbert, Jérôme Renault, Sylvain Sorin, Xavier Venel, Wieslaw Zielonka. On the values of repeated games with signals. The Annals of Applied Probability, 2016, 26 (1), pp.402-424. ⟨10.1214/14-AAP1095⟩. ⟨hal-01006951⟩