A differential game model for sponsored content
研究了高质量内容平台中传统广告与赞助广告（原生广告）的博弈，媒体需权衡广告收益与信誉损失，通过Stackelberg微分博弈找到均衡条件。
We consider a communication platform distinguished for its high-quality content, where advertising can take two different forms: traditional and sponsored (also known as native advertising in the marketing literature). Native advertising is a widely used marketing tool that aims to mimic the regular topics of the platform on which it is placed. Due to this striking resemblance, native advertising may be very effective, but at the same time, it may negatively influence the perceived credibility of the media outlet. In our model, a firm allocates investments to both traditional and native advertising on such a platform. Meanwhile, the media outlet must grapple with the trade-off between the profit accrued from publishing native advertising and the ensuing decline in credibility. We formalise this problem as a hierarchical infinite-time horizon linear state differential game, played à la Stackelberg, where the media outlet acts as the leader while the firm is the follower. Finally, we characterise a time-consistent open-loop equilibrium and obtain the conditions that make it optimal for the media outlet to accept native advertising.