Algorithms increasingly serve as information mediators--from social media feeds and targeted advertising to the increasing ubiquity of LLMs. This engenders a joint process where agents combine private, algorithmically-mediated signals with learning from peers to arrive at decisions. To study such settings, we introduce a model of controlled sequential social learning in which an information-mediating planner (e.g. an LLM) controls the information structure of agents while they also learn from the decisions of earlier agents. The planner may seek to improve social welfare (altruistic planner) or to induce a specific action the planner prefers (biased planner). Our framework presents a new optimization problem for social learning that combines dynamic programming with decentralized action choices and Bayesian belief updates. We prove the convexity of the value function and characterize the optimal policies of altruistic and biased planners, which attain desired tradeoffs between the costs they incur and the payoffs they earn from induced agent choices. Notably, in some regimes the biased planner intentionally obfuscates the agents' signals. Even under stringent transparency constraints--information parity with individuals, no lying or cherry-picking, and full observability--we show that information mediation can substantially shift social welfare in either direction. We complement our theory with simulations in which LLMs act as both planner and agents. Notably, the LLM planner in our simulations exhibits emergent strategic behavior in steering public opinion that broadly mirrors the trends predicted, though key deviations suggest the influence of non-Bayesian reasoning consistent with the cognitive patterns of both humans and LLMs trained on human-like data. Together, we establish our framework as a tractable basis for studying the impact and regulation of LLM information mediators.

翻译：算法日益成为信息中介——从社交媒体推送和定向广告到日益普及的大型语言模型（LLM）。这催生了一种联合过程：智能体将私有的、经算法中介的信号与从同伴处学习的信息相结合以做出决策。为研究此类场景，我们提出了一种受控序贯社会学习模型，其中信息中介规划者（如LLM）控制智能体的信息结构，同时智能体也从前序智能体的决策中学习。规划者可能旨在提升社会福利（利他型规划者），或诱导智能体采取规划者偏好的特定行动（偏见型规划者）。我们的框架提出了一个社会学习的新优化问题，该问题将动态规划与分散式行动选择及贝叶斯信念更新相结合。我们证明了价值函数的凸性，并刻画了利他型与偏见型规划者的最优策略，这些策略在规划者承担的成本与从诱导智能体选择中获得的收益之间实现了期望的权衡。值得注意的是，在某些机制下，偏见型规划者会故意混淆智能体的信号。即使在严格的透明度约束下——与个体信息对等、禁止撒谎或选择性呈现信息、完全可观测——我们证明信息中介仍能显著地朝任一方向改变社会福利。我们通过模拟实验补充理论分析，其中LLM同时扮演规划者与智能体的角色。值得注意的是，模拟中的LLM规划者在引导公众意见时表现出新兴的战略行为，其大体趋势与理论预测相符，但关键偏差表明非贝叶斯推理的影响，这与人类及基于类人数据训练的LLM的认知模式一致。综上，我们确立该框架为研究LLM信息中介的影响与监管提供了一个可处理的理论基础。