Limit value of dynamic zero-sum games with vanishing stage duration

We consider two person zero-sum games where the players control, at discrete times {tn} induced by a partition $Π$ of R + , a continuous time Markov state process. We prove that the limit of the values v$Π$ exist as the mesh of $Π$ goes to 0. The analysis covers the cases of : 1) stochastic games (where both players know the state) 2) symmetric no information. The proof is by reduction to a deterministic differential game.

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