A game theoretical approach to public investment versus private investment

Abstract

In this paper, private investment and public investment are modelled in a differential game framework. A feedback Nash equilibrium solution is obtained. The private saving rate and the government's income tax rate are derived as functions of time, private capital stock, and public capital stock. Their relationship with model parameters — like the discount rate, the depreciation rate, terminal valuation of capital stock, marginal product of capital and the planning horizon — are examined. Various extensions of the basic model are made.