Summary: The paper deals with the discrete-time version of Bagchi’s regional investment allocation model as a two-level Stackelberg game where a leader is the central planning board and followers are regional authorities. Each regional saving rate is determined by a discrete maximum principle under inequality constraints, maximizing its intertemporal utility function, given a tax rate and an allocation parameter. On the other hand, the central planning board will select the allocation parameter, without disturbing the reaction function of each region, so as to minimize the difference between regional capital stocks per capita and to maximize total capital stocks as a whole in the final period. Relations among capital and co-state variables are analyzed in phase diagrams, and numerical examples provide feasible series of optimum solutions for both Cobb-Douglas and CES production function cases.