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Pricing Online LLM Services with Data-Calibrated Stackelberg Routing Game

AAAI 2026 · Large language models › Reasoning and chain of thought · approach: Routing, pruning and distillation for reasoning · 0 citations (OpenAlex)

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Proposes PriLLM, a data-calibrated Stackelberg routing game with a deep aggregation network that abstracts rival LLM providers, enabling fast near-optimal real-time pricing for an LLM service provider.

Problem

Optimal dynamic pricing for a leader LLM provider in a competitive LLM routing market is an MPEC (bilevel with user-side Nash equilibrium) that is NP-hard and too slow for real-time use, and existing models ignore subjective user preferences and congestion.

Approach

Models LLM routing as a Stackelberg congestion game with objective (price, delay, congestion) and subjective (perceived value b_j) terms, calibrates parameters on OpenRouter traffic via differentiable equilibrium prediction, and uses a set-attention-based deep aggregation network to compress rival providers into K-1 kept plus one aggregated rival before solving the MPEC.

Key results

• PriLLM achieves 95.1%-98.5% of optimal profit across four market scenarios, with 1.04-4.95 s computation time.
• Calibration on the coding market reaches R^2 of 0.8982 and MAE of 3.56M tokens.
• With 8 LLMs, DA K=2 reaches 95.2%/94.5% profit versus 100% for brute force, while K=3 reaches 99.7%/99.5%.

Surprising findings

• A provider's price increase can expand its market share if accompanied by substantial performance improvements.
• Using K=1 aggregated rival yields only 93.8% profit, and naive MIN or AVG aggregation drops profit to below 60% or below 20%.

Limitations

• Single-leader formulation; multi-leader competition left to future work.
• Relies on the assumption that observed weekly routing flows are user-side Nash equilibria.
• Evaluation uses simulated QoS and user-specific TTFT sampled from observed distributions, and user perceived values are inferred rather than observed.

Experimental setup

Datasets: OpenRouter APP usage data (Apr-Jul 2025) OpenRouter LLM performance data (Jul 2025)

Benchmarks: OpenRouter market scenarios (Premium, Economy, Coding, Translation)

Metrics: profit relative to optimal (%) computation time (s) R^2 MAE MSE

Baselines: pMPEC Smooth SPGCE ODCA SPITER NPM XGBoost FD A2C

Builds on: Stackelberg game Rosen uniqueness theorem Set Transformer

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