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Over the past three decades, the reach of recommender systems has grown exponentially. Today, recommender systems are deployed on all major internet platforms, influencing our opinions, decisions, careers, and relationships. However, despite their far-reaching impact, these algorithms and their consequences are still poorly understood. In this thesis, we argue that this is due to the challenging dynamics of the recommendation problem. We outline four problems that distinguish the dynamics of recommendation from other dynamical systems, making them particularly hard to reason about: (1) direct measurement and experimentation are often infeasible, (2) feedback effects make it difficult to reason about cause and effect, (3) the scale of internet platforms requires increased algorithmic complexity, and (4) incentives created by recommender systems cause users to behave strategically. We build the foundations necessary to understand and remedy these four problems, paving the way for a complete understanding of the dynamics of recommender systems and their consequences.

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