Optimal investment, financing, and dividends. A Stackelberg differential game (Q1121757)

An open loop three-player Stackelberg game, with the manager of a firm as the leader and two shareholders as followers is considered. Each shareholder maximizes the integral taxable earnings from share transactions plus dividends, and capital gains at the horizon date; the manager maximizes integral accumulated profits after corporate tax. The manager controls investments, borrowing, lending; the shareholders control the share price and dividends. Closed form results are given, with their qualitative interpretation, about an open-loop Stackelberg equilibrium. The model of the firm is a simple linear relation between the stock of capital goods, debt, and the present value of retained earnings. Only a fixed share transactions price is allowed.