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

arXiv: https://arxiv.org/abs/2305.16695 · HTML: https://mlsanity.com/paper/2305.16695/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 May 2023.

## Built on by (most cited first, 4 of 4)

- [GLEE: A Unified Framework and Benchmark for Language-based Economic Environments](https://mlsanity.com/paper/2410.05254/) (2024)
- [Data Sharing with a Generative AI Competitor](https://mlsanity.com/paper/2505.12386/) (2025)
- [RLRF: Competitive Search Agent Design via Reinforcement Learning from Ranker Feedback](https://mlsanity.com/paper/2510.04096/) (2025)
- [CHASE: How Content Ecosystems Are Reshaped When Ranking Is the Only Target](https://mlsanity.com/paper/2608.30466/) (2026)

## Abstract (arXiv)

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.