Markov perfect equilibrium in multi-period games between sponsor and bureau

We formulate a simple model of the interaction between a sponsor and a bureau. The sponsor sets the bureau's budget while the bureau decides on how much to spend on slack. We compute numerically Markov perfect equilibria of multi-period games where the agents move alternately and apply Markov strategies. Both agents are worse off compared to the one-period game with simultaneous moves. As the discount factors increase, the equilibrium outcome becomes less cooperative in nature.