Fuzzy Option In R&D Investment Games Between Two Asymmetric Firms

R&D projects have the characteristic with uncertainty, irreversibility, long-term and competitiveness. The asymmetric investment information will also influence the decision maker. The evaluation of R&D projects will be affected by lots of factors including the subjective and objective factors. Under the uncertain environment, the factors character with not only random, but also fuzzy. In the view point of objective factors, as some variable cannot be described by précised data, the information and data from observation and statistics will be different from the actual, which leads to the uncertainty. In the view of subjective factors, in the process of evaluation of R&D projects, people will have the subjective judgments which effect the right decision to be made. So, in actual, the pricing problem of R&D project character with not only random but also fuzzy, and random and fuzzy cannot be replaced by each other. Considering this situation, I hope I can combine the fuzzy theory, real option theory and stochastic theory together to form a model so as to do a better and more comprehensive evaluation of R&D projects.At first, I conclude the research about this field in recently and introduce some basic theories which will be used in this research. And then, I conclude the traditional evaluation method and analyze their strength and weakness. So it is seem the random plus fuzzy model will be very suitable for R&D projects. After that, based on the previous research by others, I establish model between two asymmetric firms under uncertainty, which based on the model of Black-Scholes and fuzzy theory. According to the fuzzy expansion operation, I solved the value function of follower and leader and the interval of the optimal investment threshold of risk neutral decision maker. On the base of solution, I analyze the investment threshold, which focuses on the condition of the optimal investment threshold and some characteristics. And then, I get the way to the optimal investment threshold to certain decision maker by putting the subjective opinion of decision maker into the analysis.The analysis above provides a new evaluation method and theory tool for the analysis of the R&D investment decision, which has economic and strategic meaning.