Repeated Games with Incomplete Information over Predictable Systems

Ehud Lehrer*, Dimitry Shaiderman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Consider a stationary process taking values in a finite state space. Each state is associated with a finite one-shot zero-sum game. We investigate the infinitely repeated zero-sum game with incomplete information on one side in which the state of the game evolves according to the stationary process. Two players, named the observer and the adversary, play the following game. At the beginning of any stage, only the observer is informed of the state ξn and is therefore the only one who knows the identity of the forthcoming one-shot game. Then, both players take actions, which become publicly known. The paper shows the existence of a uniform value in a new class of stationary processes: ergodic Kronecker systems. Techniques from ergodic theory, probability theory, and game theory are employed to describe the optimal strategies of the two players.

Original languageEnglish
Pages (from-to)834-864
Number of pages31
JournalMathematics of Operations Research
Issue number2
StatePublished - May 2023


FundersFunder number
Deutsche ForschungsgemeinschaftKA 5609/1-1
Israel Science Foundation591/21


    • Kronecker systems
    • incomplete information on one side
    • irrational rotation of the unit circle
    • odometers
    • repeated games
    • stationary processes
    • uniform value


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