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Based on the model of symmetric and asymmetric duopoly option game, this paper discusses the present value of profit flows and the sunk investment costs for the trapezoidal fuzzy number. It constructs the fuzzy expressions of the investment value and investment threshold of followers and leaders under fuzzy environment and conducts numerical analysis. This offers a kind of explanation to the investment strategies under fuzzy environment.

Under the condition of uncertain symmetric duopoly game model, the model was firstly proposed by Smets [

The concept of fuzzy set was initiated by Zadeh [

A fuzzy set

Let

From Carlsson and Fullér [

This paper reviews the symmetrical and asymmetrical enterprises technology innovation investment decision problem under fuzzy environment, discusses the model under fuzzy environment, and concludes followers’ and leaders’ fuzzy expression of the investment and the critical value under fuzzy environment. By the technology of fuzzy simulation and data, we can find that the symmetrical and asymmetrical enterprises have the optimal investment strategy under fuzzy environment.

Assuming that there exist two technology innovation investment enterprises with neutral and rational risk in market and assuming that both of them have opportunities of technology innovation and irreversible investment, where such investment opportunity exists forever, their competition and strategies are both symmetrical. The sunk investment cost

If the investment can increase the expected income stream and have advantage of the first mover, the following restrictions on

Further, we assume that there is a first mover advantage to investment

According to the calculation rules of the trapezoidal fuzzy number, the solution

Similar with the followers’ discussion, we have the leading value function

When there does not exist an initial investment, the critical value of the optimal investment strategy in a critical point is

When there exists an initial investment,

Under imperfect competition environment, the thought of the investment cost asymmetry investment decision-making’s model is from the Grenadier’s [

Here,

When the leader has invested, investment value of followers is the combination of the profit stream

From Dixit and Pindyck [

According to the method from the literature [

The optimal investment strategy of followers to invest is at the time of

Under fuzzy environment, the value function and monopoly investment threshold of the enterprise

Under the situation of two companies investing at the same time, the value of each enterprise investment

The optimal investment strategy of two businesses is to invest at the time of

When

At the same time, influenced by

When

When

Due to space limitations, we do not use the fuzzy simulation method to compute. This method can be found in [

Of course, when the uncertain factor of the enterprise technology innovation investment project cash flow, and the investment sunk cost of the enterprise technology innovation are trapezoidal fuzzy numbers, we consider the cost difference and balanced relationship types of operating costs of the symmetrical and asymmetrical enterprise, and obtain the value function and the corresponding threshold value of investment of the leaders and followers under fuzzy environment. Through numerical analysis, we find the symmetrical and asymmetrical enterprises under fuzzy environment still have the optimal investment strategies and make comparison. Of course, since in reality there exist the situation of symmetry and asymmetry of market demanding under fuzzy environment and technology, two or more factors, and the problems in process of dynamic stage, we will try our best to solve these problems in the future.

This work was supported by science and technology project of YuBei District, ChongQing, China, No. 2012 (social) 20.