Credit ratings are essential in capital markets, serving as a bridge to reduce information asymmetry between firms and investors. However, the prevalent issuer-pay model creates a potential conflict of interest: since CRAs are paid by the issuers, they may have incentives to inflate ratings to retain clients, compromising the credibility of ratings and threatening market stability. This concern is often linked to the observed discrepancies between solicited ratings (for paying firms) and unsolicited ratings (for non-paying firms), as documented in empirical studies.

We consider a dynamic learning and ranking problem of a digital platform. Uninformed of the products' intrinsic qualities, the platform strives to design a sequential ranking policy that learns from historical traffic data while accounting for potential manipulation by sellers to inflate their performances, which we refer to as "brushing." Are there effective yet simple ranking algorithms to combat the sellers' brushing activities?