Constrained Markov games with transition probabilities controlled by a single player

We consider a two-players zero-sum Markov game with side constraints where only one player controls the transition probabilities. We reduce the problem to that of solving an equivalent linear program. Our approach is different than the one previously used to derive such linear programs [4, 5, 9]. We introduce a new type of constraints: the”subsciption constraints” along with standard constraints which we call”realization constraints”. We extend the results obtained in [4, 5, 9] to the case where both players have constraints.