On the Convergence of No-Regret Dynamics in Information Retrieval Games with Proportional Ranking Functions

Publishers who publish their content on the web act strategically, in a behavior that can be modeled within the online learning framework. Regret, a central concept in machine learning, serves as a canonical measure for assessing the performance of learning agents within this framework. We prove that any proportional content ranking function with a concave activation function induces games in which no-regret learning dynamics converge. Moreover, for proportional ranking functions, we prove the equivalence of the concavity of the activation function, the social concavity of the induced games and the concavity of the induced games. We also study the empirical trade-offs between publishers' and users' welfare, under different choices of the activation function, using a state-of-the-art no-regret dynamics algorithm. Furthermore, we demonstrate how the choice of the ranking function and changes in the ecosystem structure affect these welfare measures, as well as the dynamics' convergence rate.