A FEEDBACK NASH EQUILIBRIUM SOLUTION FOR NONCOOPERATIVE INNOVATIONS IN A STOCHASTIC DIFFERENTIAL GAME FRAMEWORK

In this paper, a stochastic model of non-cooperative technological innovations is developed. A feedback Nash equilibrium solution is obtained and the equilibrium innovation strategies are derived in explicit form. Several interesting properties of the equilibrium strategies are observed. On the one hand, an increase in the degree of competition in the industry, in the discount rate or in the state of technology reduces innovation efforts. On the other hand, an increase in the rate of degradation of the state of technology due to obsolescence results in an increase in innovation investment. While an increase in uncertainty reduces the expected present value of present and future discounted profits innovation efforts increase as uncertainty increases.