The widespread adoption of Large Language Models (LLMs) through Application Programming Interfaces (APIs) induces a critical vulnerability: the potential for dishonest manipulation by service providers. This manipulation can manifest in various forms, such as secretly substituting a proclaimed high-performance model with a low-cost alternative, or inflating responses with meaningless tokens to increase billing. This work tackles the issue through the lens of algorithmic game theory and mechanism design. We are the first to propose a formal economic model for a realistic user-provider ecosystem, where a user can iteratively delegate $T$ queries to multiple model providers, and providers can engage in a range of strategic behaviors. As our central contribution, we prove that for a continuous strategy space and any $ε\in(0,\frac12)$, there exists an approximate incentive-compatible mechanism with an additive approximation ratio of $O(T^{1-ε}\log T)$, and a guaranteed quasi-linear second-best user utility. We also prove an impossibility result, stating that no mechanism can guarantee an expected user utility that is asymptotically better than our mechanism. Furthermore, we demonstrate the effectiveness of our mechanism in simulation experiments with real-world API settings.

翻译：通过应用程序编程接口广泛采用大型语言模型引发了一个关键漏洞：服务提供商可能进行不诚实的操纵。这种操纵可能表现为多种形式，例如秘密地将宣称的高性能模型替换为低成本替代品，或在响应中填充无意义标记以增加计费。本研究通过算法博弈论和机制设计的视角解决这一问题。我们首次为现实的用户-提供商生态系统提出了正式的经济模型，其中用户可以迭代地将$T$个查询委托给多个模型提供商，而提供商可以采取一系列策略行为。作为核心贡献，我们证明了对于连续策略空间和任意$ε\in(0,\frac12)$，存在一个近似激励相容机制，其具有$O(T^{1-ε}\log T)$的加性近似比，并保证准线性的次优用户效用。我们还证明了一个不可能性结果：没有任何机制能保证渐近优于我们机制的期望用户效用。此外，我们在真实API设置的模拟实验中验证了该机制的有效性。