研究大模型推理服务中默认分配与定价如何影响用户选择。
Keep, Customize, or Exit: Default Design and Token Pricing in LLM Reasoning Services
- 构建斯塔克伯格博弈模型，推导用户最优自定义分配策略。
- 发现默认配置仅在用户重视便捷时才影响实际使用量。
- 实验验证模型在数学科学任务中可精准预测最优价格与分配。
我们研究一种大语言模型（LLM）服务，其中服务提供商设定每令牌价格和默认推理令牌分配，用户可接受默认、自定义分配或退出。更大的分配可提升准确率但增加令牌成本与延迟。我们将该互动建模为斯塔克伯格博弈，推导出用户唯一最优自定义分配的闭式解。对于任意价格，可接受的默认配置构成空集或紧区间。我们通过三区制规则刻画了提供商的最优默认设置，将均衡计算简化为一维价格优化，并证明均衡存在性。进一步表明，只有当用户重视避免自定义的便利性时，默认配置才会影响实际实施的推理分配；否则，所有服务结果均实现用户的最优自定义分配。在两个小型开源推理模型上，于五个数学与科学基准测试中的实验支持了准确率-令牌模型，并揭示模型与任务特性如何决定均衡价格、默认值与推理分配。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。