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 {t_n} induced by a partition Π of ℝ⁺, a continuous time Markov process. We prove that the limit of the values υ_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), and (2) games with unknown state and symmetric signals.

The proof is by reduction to deterministic differential games.