Stochastic Evolutionary Game Analysis of Price Cheating Using Milstein Method and Numerical Simulations

The frequent occurrence of price cheating on remanufactured products has seriously affected the healthy development of remanufactured products market. And there are many uncertainties in society that greatly affect the behavioral decisions of market participants. Therefore, it is necessary to study the price cheating of remanufactured products under random interference. Firstly, we introduce Gaussian white noise as random interference and construct a stochastic evolutionary game of sellers, consumers and the government. Secondly, we analyze stability conditions of the system by using the stability discriminant theorem for stochastic differential equation. Finally, we numerically solve the model using Milstein method and perform numerical simulations to analyze the factors affecting evolutionary paths of the system. Some important results are obtained. i) Decisions of sellers, consumers and the government fluctuate up and down by random interference. The greater the intensity of random interference is, the greater the fluctuations of decisions are. ii) Under same conditions, sellers are the fastest to evolve to choose not to disguise, the government is the second fastest to evolve to choose not to strictly inspect, and consumers are the slowest to evolve to choose green consumption. iii) Increasing consumer acceptance of remanufactured products, consumers' willingness to pay for remanufactured products, and consumer discrimination can prompt sellers to choose not to disguise.