Optimal incentive strategy in a discounted stochastic Stackelberg game

We consider a game where manager's (leader's) aim is to maximize the gain of a large corporation by the distribution of funds between $m$ producers (followers). The manager selects a tuple of $m$ non-negative incentive functions, and the producers play a discounted stochastic game, which results in a Nash equilibrium. Manager's aim is to maximize her related payoff over the class of admissible incentive functions. It is shown that this problem is reduced to a Markov decision process.