Application of game theory on parameter optimization of the novel two-stage Nash nonlinear grey Bernoulli model

• This paper combine game theory and two-stage nonlinear grey forecasting model which is novel.
• The results show its feasibility of increasing forecasting precision.

In grey prediction modeling, there are three parameters in nonlinear grey Bernoulli model (NGBM), including the power n, the coefficient p and the length of raw data used to construct grey forecasting model. Nash NGBM only optimizes n and p by the iterated elimination of weakly dominated strategies of game theory. To optimize above three parameters, this study develops a two-stage game for NNGBM (abbreviated as two-stage NNGBM). In the first stage, find the Nash equilibrium for each possible game. In the second stage, use Minimax principle to find the optimal left topological sequence which has the best forecasting performance. Then, obtain Nash equilibrium which consists of these three parameters. This study also proves that the traditional GM(1, 1), optimal p GM(1, 1) and NGBM(1, 1) are the special cases of the proposed model. In order to show the feasibility of this research, the proposed method is applied to the forecasting of Taiwan’s GDP. The results show that five elements in raw data sequence are optimal topological length for constructing NNGBM in the case of Taiwan’s GDP forecasting.