We consider a two-player stochastic dynamic game in discrete time and space, with infinite horizon and discount. The game is played in a Stackelberg way with stationary feedback strategies. The leader announces a strategy and the follower reacts optimally. Strategies solution to the problem correspond to value functions solution to a certain dynamic programming operator. We identify families of problems for which an unique solution does exist. We also exhibit cases where no solution exist, and cases where solutions do exist but Value Iteration does not converge.

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