TY - JOUR
T1 - Repeated Games with Incomplete Information over Predictable Systems
AU - Lehrer, Ehud
AU - Shaiderman, Dimitry
N1 - Publisher Copyright:
© 2022 INFORMS.
PY - 2023/5
Y1 - 2023/5
N2 - 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.
AB - 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.
KW - Kronecker systems
KW - incomplete information on one side
KW - irrational rotation of the unit circle
KW - odometers
KW - repeated games
KW - stationary processes
KW - uniform value
UR - http://www.scopus.com/inward/record.url?scp=85161029402&partnerID=8YFLogxK
U2 - 10.1287/moor.2022.1286
DO - 10.1287/moor.2022.1286
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AN - SCOPUS:85161029402
SN - 0364-765X
VL - 48
SP - 834
EP - 864
JO - Mathematics of Operations Research
JF - Mathematics of Operations Research
IS - 2
ER -