Differential Games between a Brand Manufacturer and an Internet Celebrity Regarding Fairness Concerns

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With the rapid growth of social media and live-streaming technology, live-stream selling has become integral to the digital economy. Using differential game theory, this paper examines how fairness concerns impact the profits of internet celebrities and brand manufacturers under the “pure commission” model. We analyzed no fairness concern, gap fairness concern, and self-due fairness concern models, to investigate the optimal decisions and corresponding profits for an internet celebrity and a brand manufacturer. The results show that the internet celebrity earned the highest profits with low commission rates under the self-due fairness concern model, whereas higher commission rates yielded higher profits for the internet celebrity under the gap fairness concern model. Simultaneously, fairness concerns significantly affected the cooperation stability and long-term benefits, motivating the internet celebrity to maintain efficient collaborations with the brand manufacturer. Furthermore, the self-due fairness concern model was more practical than the gap fairness concern model.