Skip to Main content Skip to Navigation
Journal articles

Existence of the uniform value in zero-sum repeated games with a more informed controller

Abstract : We prove that in a general zero-sum repeated game where the first player is more informed than the second player and controls the evolution of information on the state, the uniform value exists. This result extends previous results on Markov decision processes with partial observation (Rosenberg, Solan, Vieille 2002), and repeated games with an informed controller (Renault 2012). Our formal definition of a more informed player is more general than the inclusion of signals, allowing therefore for imperfect monitoring of actions. We construct an auxiliary stochastic game whose state space is the set of second order beliefs of player 2 (beliefs about beliefs of player 1 on the true state variable of the initial game) with perfect monitoring and we prove it has a value by using a result of Renault 2012. A key element in this work is to prove that player 1 can use strategies of the auxiliary game in the initial game in our general framework, which allows to deduce that the value of the auxiliary game is also the value of our initial repeated game by using classical arguments.
Document type :
Journal articles
Complete list of metadatas

Cited literature [14 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00772043
Contributor : Fabien Gensbittel <>
Submitted on : Wednesday, January 9, 2013 - 6:27:12 PM
Last modification on : Wednesday, December 9, 2020 - 3:46:09 AM
Long-term archiving on: : Wednesday, April 10, 2013 - 3:56:24 AM

Files

moreinfoF3.pdf
Files produced by the author(s)

Identifiers

Citation

Fabien Gensbittel, Miquel Oliu-Barton, Xavier Venel. Existence of the uniform value in zero-sum repeated games with a more informed controller. Journal of Dynamics and Games (JDG), Springer, 2014, 1 (3), pp.411-445. ⟨10.3934/jdg.2014.1.411⟩. ⟨hal-00772043⟩

Share

Metrics

Record views

836

Files downloads

724