Dynamic model of R&D investment and technology stock under rivalry by differential game

Abstract

This study is to develop a quantitative model which reflects dynamic characteristics of R/D investment existing between the technological leader and follower under competitive situation. Two rivals`` R\&D investment is formulated as the differential game which reflects rival``s investment strategy to the other``s. By applying optimal control theory to this differential game, it is possible to find the necessary conditions for Nash equilibrium. Two types of solutions are found on the conditions: noninteractive and interactive solutions. As a result of analysis this study presents the evaluation rules for R\&D investment alternatives under rivalry. It is also possible to establish the strategy for R\&D investment taking advantage of rival``s investment behaviour.