Pricing Online LLM Services with Data-Calibrated Stackelberg Routing Game

TL;DR

This paper introduces extbackslash PriLLM, a scalable, real-time pricing solution for LLM services modeled as a Stackelberg game, balancing profit maximization and computational efficiency.

Contribution

It presents a novel deep learning-based approach for dynamic LLM pricing that captures market dynamics and user preferences while ensuring scalability and interpretability.

Findings

Achieves over 95% of optimal profit in experiments.

Requires less than 5% of the computation time of optimal solutions.

Effectively models real-world market behaviors and user preferences.

Abstract

The proliferation of Large Language Models (LLMs) has established LLM routing as a standard service delivery mechanism, where users select models based on cost, Quality of Service (QoS), among other things. However, optimal pricing in LLM routing platforms requires precise modeling for dynamic service markets, and solving this problem in real time at scale is computationally intractable. In this paper, we propose \PriLLM, a novel practical and scalable solution for real-time dynamic pricing in competitive LLM routing. \PriLLM models the service market as a Stackelberg game, where providers set prices and users select services based on multiple criteria. To capture real-world market dynamics, we incorporate both objective factors (\eg~cost, QoS) and subjective user preferences into the model. For scalability, we employ a deep aggregation network to learn provider abstraction that preserve user-side equilibrium behavior across pricing strategies. Moreover, \PriLLM offers interpretability by explaining its pricing decisions. Empirical evaluation on real-world data shows that \PriLLM achieves over 95\% of the optimal profit while only requiring less than 5\% of the optimal solution's computation time.