The rapid rise of short video platform has created a broad platform for live delivery, which has become a very hot new way of shopping, so many businesses and individuals have brought goods and sold goods through various online live delivery platforms. However, some businesses sell fake and shoddy goods through live broadcasts without conscience. Based on the idea of game theory, this paper constructs a mixed strategy game model with the participation of the supervision department and merchants of short video platform, analyzes the Nash equilibrium of the mixed strategy of the game model, and further constructs a mixed strategy model with the participation of government regulators, short video platform regulators and merchants. It is found that the lower the supervision cost of short video platform and the higher the fine, the smaller the probability of merchants selling unqualified goods. The probability of strict supervision of short video platform is affected by the size of its fine; The lower the detection cost of government supervision department and the greater the reward for strict supervision of short video platform, the higher the probability of strict supervision of short video platform; The probability of random inspection by government supervision departments is influenced by its punishment, detection cost and strict supervision cost of short video platform.
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