Determinacy of Games with Stochastic Eventual Perfect Monitoring
27 Pages Posted: 17 Jan 2014
Date Written: January 14, 2014
We consider an infinite two-player stochastic zero-sum game with a Borel winning set, in which the opponent's actions are monitored via stochastic private signals. We identify two conditions of the signalling structure: Stochastic Eventual Perfect Monitoring (SEPM) and Weak Stochastic Eventual Perfect Monitoring (WSEPM). When signals are deterministic these two conditions coincide and by a recent result due to Shmaya (2011) entail determinacy of the game. We generalize Shmaya (2011)'s result and show that in the stochastic learning environment SEPM implies determinacy while WSEPM does not.
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