Abstract:

With the rapid development of China’s financial capital market， especially the trading stock market， some institutional investors （individuals or units） tend to take advantage of their own capital， information， authority or other advantages to pursue high returns and reduce losses by taking manipulative actions， such as creating market illusion， false trading， misleading trading， which seriously damages the interests of investors. All these manipulations pose a great threat to the stable operation of the financial market order. Thus， how to deepen the scientific understanding of manipulative behavior and improve the efficiency of supervision is a great challenge. The research of participants’ strategic behaviors in financial market regulation based on game theory has attracted much attention. However， most of the existing researches on financial market manipulation are based on classical game theory. Classical game theory usually assumes that the participants are completely rational and independent， and concentrates the strategy space of the participants in the real number domain. It ignores the possible entanglement between the participants in the payoff of strategy choice and the preference of strategy choice， which cannot effectively reveal the behavior rules of participants. In order to solve the above problems， based on the quantum game theory， the strategy choice of participants in extended to complex number space， and a quantum supervision game model is developed for trading stock market manipulation. On this basis， the evolution of strategic choice and entanglement of investors and regulators are analyzed. Meanwhile， the strategic preferences and behavioral rules of regulators and investors under different initial entanglement states are analyzed. The results show that： （1） After adopting the quantum strategy， the returns of both participants have been improved. It means that compared with classical games， quantum supervised games can achieve Pareto improvement of Nash equilibrium solutions. （2） The parameter in the quantum initial state， namely the degree of entanglement， is a key factor influencing the manipulation preferences of investors. The regulators can induce investors to prefer non-manipulation strategies by strengthening the entanglement between their strict supervision and investor strategy manipulation. Also， the regulators can implement dynamic regulatory strategies based on changes in the initial entangled state， thereby reducing regulatory costs while ensuring the stable operation of the market. Finally， through simulation analysis， how the initial entangled state affects the manipulation returns of investors， and then affects their manipulation behavior preferences if further studied. Accordingly， some countermeasures and suggestions are given to help regulators to improve the efficiency of market supervision.

Key words: manipulative behavior, supervisory game, quantum game, Nash equilibrium, quantum entanglement