Paper: Dütting, Mirrokni, Paes Leme, Xu, Zuo (2024), Mechanism Design for Large Language Models.论文：Dütting、Mirrokni、Paes Leme、Xu、Zuo（2024），《面向大型语言模型的机制设计》。

Research question. How should we auction influence over AI-generated content—e.g., ad creatives—when each advertiser is represented by an LLM that supplies a distribution over the next token rather than a standard valuation function? The authors propose a token auction that aggregates multiple LLMs’ next-token distributions, guided by scalar bids, to generate the final text and determine payments. 研究问题。我们应如何拍卖对 AI 生成内容（例如广告创意）的影响力——当每个广告主由一个 LLM 代表，该 LLM 提供的是下一个词元的分布而非标准的估值函数？作者提出了一种词元拍卖方法，该方法汇总多个 LLM 的下一个词元分布，并由标量出价引导，以生成最终文本并确定支付金额。

Model in brief.模型简述。

• Each agent has an LLM mapping a prompt prefix to a next-token distribution; models are stateless and generation is autoregressive. 每个代理拥有一个 LLM，将提示前缀映射到下一个词元的分布；模型无状态，生成过程为自回归。

• Agents submit one-dimensional bids; the mechanism combines the per-agent token distributions into a single distribution from which each token is sampled, and computes payments. 代理提交一维出价；机制将每个代理的代币分布合并成一个单一分布，从中抽取每个代币，并计算支付。

Preference modeling. Because full utilities over high-dimensional distributions are unrealistic, the paper adopts a robust partial order: an outcome is (weakly) better for agent i if it moves every token probability toward that agent’s preferred distribution and never in the opposite direction. This underpins two minimal incentive conditions: payment monotonicity (you pay more iff you get a closer distribution) and consistent aggregation (the rank of your own bids doesn’t depend on others’ bids). 偏好建模。由于对高维分布的完整效用建模不现实，本文采用了一种稳健的偏序：如果一个结果使每个代币的概率都朝向代理 i 偏好的分布移动，且从不朝相反方向移动，则该结果对代理 i 来说是（弱）更优的。这支撑了两个最小激励条件：支付单调性（只有当你获得更接近的分布时才支付更多）和一致聚合（你自己的出价排名不依赖于他人的出价）。

Core result (revelation-style). Any mechanism satisfying payment monotonicity and consistent aggregation is strategically equivalent to one with a monotone aggregation function: increasing your bid weakly moves the implemented distribution toward your preferred one. This reduces design to choosing monotone aggregation plus payments. 核心结果（启示式）。任何满足支付单调性和一致聚合的机制，在策略上等价于具有单调聚合函数的机制：增加你的出价会使实施的分布弱地朝向你偏好的分布移动。这将设计简化为选择单调聚合函数和支付方案。

Pricing: a second-price analogue. For any monotone aggregation rule, there exists a stable sampling implementation that yields a critical-bid (second-price-like) payment: for a given random seed, you pay the minimum bid at which the realized token would have switched from an “oversampled” token to your “undersampled” token. The expected payment admits a Myerson-style integral in terms of the reduction in total variation distance to your preferred distribution. 定价：第二价格类比。对于任何单调聚合规则，都存在一个稳定的采样实现，产生一个临界出价（二价类似）支付：对于给定的随机种子，你支付的是实现的 token 从“过采样”token 切换到你的“欠采样”token 时的最低出价。期望支付可以用 Myerson 风格的积分表示，积分内容是到你偏好分布的总变差距离的减少。

Designing the aggregation rule. Guided by LLM training losses:设计聚合规则。以 LLM 训练损失为指导：

• Pre-training–style (KL) objective: minimizing a bid-weighted sum of KL divergences from agents’ preferred distributions yields a linear (mixture) rule—the implemented next-token distribution is the bid-weighted average of agents’ distributions. This rule is monotone and thus incentive-compatible under the robust approach. 预训练风格（KL）目标：最小化代理偏好分布的 KL 散度的出价加权和，得到一个线性（混合）规则——实现的下一个 token 分布是代理分布的出价加权平均。该规则是单调的，因此在稳健方法下具有激励相容性。

• RLHF-style objective: minimizing KL from the implemented distribution to each agent’s distribution yields a log-linear (geometric mean) rule. It is optimal for that loss but not monotone, so it can violate the robust incentive conditions. RLHF 风格目标：将已实现分布与每个代理的分布之间的 KL 散度最小化，得到一个对数线性（几何平均）规则。该规则对于该损失是最优的，但不是单调的，因此可能违反稳健激励条件。

Demonstration. Using a prompt-tuned public LLM, the authors show two-advertiser examples where outputs interpolate smoothly as the bid share shifts; co-marketing produces blended ads at intermediate bids, while competing brands tend to separate. 示范。作者使用经过提示调优的公共 LLM，展示了两个广告主的示例，输出随着出价份额的变化平滑插值；联合营销在中间出价时产生混合广告，而竞争品牌则倾向于分开。

Economic interpretation and takeaways.经济解释与启示。

• The token auction treats generated text as a public project whose probabilistic content is endogenously shaped by bids. Monotonic aggregation plus the critical-bid rule delivers a clean analogue of second price in a high-dimensional, stochastic allocation environment, while requiring only ordinal (partial-order) preference information. 代币拍卖将生成的文本视为一个公共项目，其概率内容由竞标内生地塑造。单调聚合加上关键竞标规则，在高维随机分配环境中提供了一个类似于第二价格拍卖的清晰模型，同时仅需序数（部分序）偏好信息。

• The linear mixture rule is both practically simple and theoretically aligned with robust incentives; the log-linear rule trades off those incentives for a closer match to RLHF-style objectives. 线性混合规则在实际操作上既简单又与稳健激励理论相符；而对数线性规则则以牺牲部分激励为代价，更加贴近 RLHF 风格的目标。

Limitations acknowledged. The approach assumes access to agents’ LLMs, relies on stateless next-token preferences, and cannot guarantee a single implementation that is “universally” stable across all bid profiles. 承认存在局限性。该方法假设可以访问代理的 LLMs，依赖于无状态的下一个词偏好，且无法保证在所有出价配置下都能实现“普遍”稳定的单一实现。

If you’d like, I can add a short “economist’s toolbox” note—e.g., where this sits relative to VCG/VCG-style mechanisms and GSP in ad auctions—and a quick comparison of welfare and revenue properties under the linear vs. log-linear rules.如果您愿意，我可以添加一段简短的“经济学家工具箱”说明——例如，说明这与广告拍卖中的 VCG/VCG 风格机制和 GSP 的关系——以及线性规则与对数线性规则下福利和收入特性的快速比较。