Abstract
We revisit the Dynkin game problem in a general framework and relax some assumptions. The pay-offs and the criterion are expressed in terms of families of random variables indexed by stopping times. We construct two non-negative supermartingale families J and whose finiteness is equivalent to the Mokobodski's condition. Under some weak right-regularity assumption on the pay-off families, the game is shown to be fair and is shown to be the common value function. Existence of saddle points is derived under some weak additional assumptions. All the results are written in terms of random variables and are proven by using only classical results of probability theory.
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