Reconstruction of public finance in a stochastic differential game framework

Abstract

In the past decade, there is an emerging trend for the use of game theoretical framework in studying government tax plicies. The game theoretical approach allows the possibility of simultaneous interactions between government policy and decentralized private decisions. This paper develops a stochastic differential game between the government and the public. The public chooses an investment strategy to maximize the present value of income net of tax and investment expenditures. The government controls the tax system and aims at maximizing a weighted sum of tax collected, the level of bonds outstanding and income net of investment expenditures. Two dynamic processes — one for the capital formation and the other for bonds accumulation — are present in the model. The dynamic processes are subject to stochastic shocks. A feedback Nash equilibrium solution of the game is obtained. The parabolic partial differential equations characterizing the value functions of the game equilibrium is solved explicitly. Closed-from solutions of the equilibrium investment strategy and tax policy are provided. The stationary (longrun equilibrium) joint density function of capital stock and bonds is also obtained.