Learning to Rank under Strategic "Brush Wars"

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?

We provide a positive answer by proposing a simple ranking algorithm termed Experiment-Then-Commit (ETC). We study the sellers' strategic responses to the ranking algorithm by formulating a multi-player and dynamic "brush war" game. We find that when the number of sellers becomes large and the time horizon becomes long, the brush war converges to a static non-atomic market model with a continuum of sellers. We provide nonasymptotic guarantees of the convergence rate and characterize a self-reinforcing market equilibrium in simple closed form. In equilibrium, brushing is proportional to quality, making it easy to learn the true ranking of sellers. As a result, a simple solution can work surprisingly well for the seemingly daunting problem. We also discuss the managerial implications.

The full paper is available at SSRN: https://ssrn.com/abstract=4854583.