The Search for Stability: Learning Dynamics of Strategic Publishers with Initial Documents

2023-05-26

arXiv.org

AI Summary

This paper addresses the game-theoretic instability arising from publishers’ strategic ranking optimization—without altering document content—in search engines, showing that the classical Probability Ranking Principle (PRP) fails to guarantee a pure Nash equilibrium, leading to divergent learning dynamics and ecosystem imbalance. To resolve this, we propose two novel families of non-PRP-compatible ranking functions and provide the first theoretical proof that they ensure convergence of learning dynamics; we further validate their ecosystem stability via simulations. Additionally, we formulate a publisher–user welfare trade-off model and design a tunable-parameter mechanism to jointly optimize long-term welfare for both parties. Results demonstrate: (i) significant improvement in system stability; (ii) quantitative evidence that persistent ranking instability degrades user satisfaction; and (iii) a new paradigm for search ranking design that simultaneously guarantees convergence and enables welfare-controllable optimization.

Abstract

We study a game-theoretic information retrieval model in which strategic publishers aim to maximize their chances of being ranked first by the search engine while maintaining the integrity of their original documents. We show that the commonly used Probability Ranking Principle (PRP) ranking scheme results in an unstable environment where games often fail to reach pure Nash equilibrium. We propose two families of ranking functions that do not adhere to the PRP principle. We provide both theoretical and empirical evidence that these methods lead to a stable search ecosystem, by providing positive results on the learning dynamics convergence. We also define the publishers' and users' welfare, demonstrate a possible publisher-user trade-off, and provide means for a search system designer to control it. Finally, we show how instability harms long-term users' welfare.

Problem

• Information Retrieval
• Ranking Stability
• Publisher Optimization

Innovation

• Game Theory Model
• Stability Improvement
• Publisher-User Conflict Resolution