In each stage of a repeated game with private monitoring, the players receive payoffs and privately observe signals which depend on the players' actions and the state of world. I show that, contrary to a widely held belief, such games admit a recursive structure. More precisely, I construct a...

The paper provides a notion of measurability for Multiple Prior Models characterized by nonatomic countably additive priors. A notable feature of our definition of measurability is that an event is measurable if and only if it is unambiguous in the sense of Ghirardato, Maccheroni and Marinacci...