Stability in Competitive Search with Results Diversification

2026-06-08

AI Summary

In competitive search environments, publishers strategically optimize their documents to improve rankings, leading to corpus instability and a fundamental trade-off between result diversification and system stability. This work employs game-theoretic modeling to analyze how diversification mechanisms affect equilibrium outcomes, revealing that existing diversified ranking methods fail to guarantee convergence to a stable state. Building on this insight, the paper proposes the first framework for designing diversified ranking functions that provably ensure corpus stability. Through rigorous equilibrium analysis and algorithmic construction, the approach effectively balances diversity and stability, addressing a critical limitation in current retrieval systems.

Abstract

In a competitive search setting, publishers strategically modify their documents in response to induced rankings so as to improve their future ranking. We present a novel game-theoretic analysis of a competitive search setting where search-results diversification is applied. Our analysis reveals an inherent tradeoff between corpus diversity and corpus stability, where the latter corresponds to an equilibrium in a game. We analyze two representative diversification methods and show that stability need not necessarily be reached, leaving the corpus to rapid changes due to ranking incentivized modifications of publishers. We then present a novel approach to devise diversification-based ranking functions that are guaranteed to lead to corpus stability.

Problem

• competitive search
• results diversification
• corpus stability
• ranking equilibrium
• strategic document modification

Innovation

• competitive search
• results diversification
• corpus stability
• game-theoretic analysis
• ranking equilibrium