Keep, Customize, or Exit: Default Design and Token Pricing in LLM Reasoning Services

2026-08-13

AI Summary

This study addresses the joint design of default resource allocation and per-token pricing in large language model inference services, aiming to balance users’ trade-offs among accuracy, cost, and latency while accounting for their choices to adopt defaults, customize configurations, or opt out. By formulating a Stackelberg game between the service provider and heterogeneous users, the work characterizes, for the first time, an equilibrium mechanism encompassing these three user behaviors, derives a closed-form solution for customized configurations, and establishes the existence of equilibrium. Theoretical analysis reveals that the default mechanism influences actual resource allocation only when users value the convenience of avoiding customization, and that equilibrium computation reduces to a one-dimensional price optimization problem. Experiments on two open-source models and five benchmark tasks validate the accuracy–token cost model and demonstrate that optimal pricing, default settings, and resource allocation are jointly determined by model and task characteristics.

Abstract

We study a large language model (LLM) service in which a provider chooses a per-token price and a default reasoning-token allocation, while a user may accept the default, customize the allocation, or exit. Larger allocations can improve accuracy but increase token cost and latency. We model this interaction as a Stackelberg game and derive the user's unique optimal customized allocation in closed form. For any price, the acceptable defaults form either an empty set or a compact interval. We characterize the provider's optimal default through a three-regime rule, reduce equilibrium computation to a one-dimensional price optimization, and prove the existence of the equilibrium. We further show that defaults affect the implemented reasoning allocation only when users value the convenience of avoiding customization; otherwise, every service-providing outcome implements the user's optimal customized allocation. Experiments with two compact open-weight reasoning models on five mathematics and science benchmarks support the accuracy-token model and show how model and task characteristics determine equilibrium prices, defaults, and reasoning allocations.

Problem

• LLM reasoning services
• default design
• token pricing
• user customization
• Stackelberg game

Innovation

• Stackelberg game
• token pricing
• default design
• reasoning allocation
• LLM service