Convergence of Learning Dynamics in Information Retrieval Games

Abstract

We consider a game-theoretic model of information retrieval with strategic authors. We examine two different utility schemes: authors who aim at maximizing exposure and authors who want to maximize active selection of their content (i.e., the number of clicks). We introduce the study of author learning dynamics in such contexts. We prove that under the probability ranking principle (PRP), which forms the basis of the current state-of-the-art ranking methods, any betterresponse learning dynamics converges to a pure Nash equilibrium. We also show that other ranking methods induce a strategic environment under which such a convergence may not occur.

Learning with Exposure Constraints in Recommendation Systems

“…Our motivation stems from previous work on strategic behavior in Machine Learning [13,14,16,20,25,37,47], and more specifically on strategic publishing [2,42]. This line of work adopts a game-theoretic perspective and analyzes equilibrium behavior [1,19].…”

“…We further denote by K t ⊆ K the subset of arms that are still available in round t. 2 Mathematically, the exposure constraint is modeled as follows. An arm a ∈ K t is viable in round t if in every phase prior to the current phase ⌊ t /τ⌋ + 1, arm a received at least δ a pulls.…”

“…Observing that an RS's recommendation policy affects content providers, several works address content providers' incentives and develop RSs that incorporate their strategic behavior [32,46]. For instance, Ben-Porat et al [2] consider content provider deviations to produce more revenue-effective items to increase their revenue. Furthermore, Mladenov et al [31] model the dependency of content providers on user engagement to create revenue and finance their operation.…”

From Recommendation Systems to Facility Location Games

“…Nevertheless, they neither a) provide a systematic approach for doing so under PNE profiles; nor b) show that a PNE always exists. Recently, Ben-Porat, Rosenberg, and Tennenholtz (2018) claim in favor of no intervention in a similar model, and show that no intervention policy leads to convergence of any better-response dynamics; thus, a PNE is guaranteed to exist. Importantly, Ben-Basat, Tennenholtz, and Kurland (2017) as well as Ben-Porat, Rosenberg, and Tennenholtz (2018) do not consider the task of mediator design for better outcomes.…”

“…The work of Ben-Porat and Tennenholtz (2018a) is the first to consider mediator design in recommendation systems with strategic content providers, in a mathematical model that extends that of Ben-Basat, Tennenholtz, and Kurland (2017) and Ben-Porat, Rosenberg, and Tennenholtz (2018). They highlight several fairness-related properties that a mediator should arguably satisfy, along with the requirement of PNE existence.…”