where κ denotes the amplitude of noise level, where κ = 0 presents determinate imitation, while κ = ∞ indicates stochastic imitation. In this paper, we will not investigate the effects of κ further, but set κ to be 0.1. In the proposed model, we assign that ifW1 > 0.5, the stochastic player would imitate the strategy of y, otherwise keep its own strategy.
Note that the decision is not affected by the variation of accumulated payoff involving the change in the surroundings. Starting from a randomly initial state, the above process is repeated many times.