Interactions between government and firms: a differential game approach

In this paper we study an extended version of the model described by Gradus in order to determine the optimal taxation policy of a government and its effects on the stock of capital goods growth as a result of the activity developed by firms. It is shown that, by introducing a wealth tax, there exists an optimal wealth tax rate for which the open-loop/feedback Nash/Stackelberg equilibria coincide, maximizing the payments for both agents (government and firms), so that the open-loop Stackelberg equilibrium becomes both time consistent and subgame perfect.