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 on
e-period game with simultaneous moves. As the discount factors increas
e, the equilibrium outcome becomes less cooperative in nature.