From Recommendation Systems to Facility Location Games

TL;DR

This paper introduces a mediator framework in facility location games to improve social welfare in recommendation systems with strategic content providers, balancing optimality and minimal intervention.

Contribution

It proposes a mediator design that achieves high social welfare at equilibrium with minimal intervention, including a case study with a socially optimal mediator in one-dimensional settings.

Findings

Proposed a mediator that enforces socially optimal equilibrium.

Bounded the intervention cost of the mediator.

Extended the framework with additional considerations and open questions.

Abstract

Recommendation systems are extremely popular tools for matching users and contents. However, when content providers are strategic, the basic principle of matching users to the closest content, where both users and contents are modeled as points in some semantic space, may yield low social welfare. This is due to the fact that content providers are strategic and optimize their offered content to be recommended to as many users as possible. Motivated by modern applications, we propose the widely studied framework of facility location games to study recommendation systems with strategic content providers. Our conceptual contribution is the introduction of a $\textit{mediator}$ to facility location models, in the pursuit of better social welfare. We aim at designing mediators that a) induce a game with high social welfare in equilibrium, and b) intervene as little as possible. In service of the latter, we introduce the notion of $\textit{intervention cost}$, which quantifies how much damage a mediator may cause to the social welfare when an off-equilibrium profile is adopted. As a case study in high-welfare low-intervention mediator design, we consider the one-dimensional segment as the user domain. We propose a mediator that implements the socially optimal strategy profile as the unique equilibrium profile, and show a tight bound on its intervention cost. Ultimately, we consider some extensions, and highlight open questions for the general agenda.