Game Model Of Innovation R&D Investment Of Duopoly Under Financing Constraint

Product innovation and R&D has become an important means of competition among enterprises,but most enterprises face financing constraints,the randomness of the success of innovation and R&D,the uncertainty of the future income of R&D projects and other problems in the process of innovation and R&D,which urges enterprises to seek R&D cooperation.Although many scholars have discussed the impact of financing constraints on enterprise innovation R&D investment decision,most scholars have not discussed the impact of financing constraints on enterprise innovation R&D investment decision under the background of duopoly.In view of this,considering the financial situation,the product scale of the established market and the bankruptcy risk,this thesis analyzes the non cooperative innovation R&D and cooperative innovation R&D of duopoly enterprises,establishes a piecewise deterministic game model by comprehensively using the dynamic programming method and the symmetric differential game theory,and discusses the impact of financing constraints on the investment decision of enterprise innovation R&D.The main research contents are as follows:Firstly,under the background of duopoly competition,this thesis analyzes the R & D decision-making of non cooperative innovation under financing constraints.In the first stage,Cournot’s output competition model is used to solve the output problem of enterprises.In the second stage,it is assumed that the transfer of enterprises between modes conforms to the Markov process.Through the dynamic programming method,a multi-mode differential game model of interaction between enterprises is constructed,and the Hamilton Jacobi Bellman(HJB)equation satisfied by the value function of enterprises in each mode is derived,The optimal R & D strategy of each enterprise under financing constraints is obtained.The research shows that: first,the enterprises with successful innovation and R & D have greater interests in the post innovation stage than those with unsuccessful innovation and R & D.at the same time,if the enterprises with successful R & D accumulate too much debt in the R & D stage,they will face greater bankruptcy risk in the post R & D stage;Second,financing constraints will inhibit the intensity of innovation and R & D investment.Secondly,continue to introduce cooperative R & D in the duopoly competitive market,and analyze the cooperative R & D decision-making of duopoly enterprises under financing constraints.A game model for cooperative R & D decision-making of duopoly enterprises under financing constraints is constructed by using the dynamic programming method.For cooperative R & D under the output based R & D input cost sharing method,when the two enterprises have the same output and allocate R & D input according to output,the R & D input shared by the two enterprises is the same,both of which are half of the total R & D input.The research shows that: first,cooperative R & D will lead to the optimal innovation R & D investment greater than that of independent innovation R & D,so the completion time of cooperative R & D will be shorter than that of independent innovation R & D;Second,cooperative R & D will restrain R & D investment in the face of bankruptcy risk,but the ability of cooperative R& D to resist bankruptcy risk is better than that of independent R & D..