We study information design in multi-agent systems (MAS) with binary actions and strategic complementarities, where an external designer influences behavior only through signals. Agents play the smallest-equilibrium of the induced Bayesian game, reflecting conservative, coordination-averse behavior typical in distributed systems. We show that when utilities admit a convex potential and welfare is convex, the robustly implementable optimum has a remarkably simple form: perfect coordination at each state: either everyone acts or no one does. We provide a constructive threshold rule: compute a one-dimensional score for each state, sort states, and pick a single threshold (with a knife-edge lottery for at most one state). This rule is an explicit optimal vertex of a linear program (LP) characterized by feasibility and sequential obedience constraints. Empirically, in both vaccination and technology-adoption domains, our constructive policy matches LP optima, scales as $O(|Θ|\log|Θ|)$, and avoids the inflated welfare predicted by obedience-only designs that assume the designer can dictate the (best) equilibrium. The result is a general, scalable recipe for robust coordination in MAS with complementarities.

翻译：本文研究具有二元行动与策略互补性的多智能体系统（MAS）中的信息设计问题，其中外部设计者仅能通过信号影响行为。智能体在诱导的贝叶斯博弈中执行最小均衡，这反映了分布式系统中典型的保守且规避协调的行为特征。我们证明，当效用函数存在凸势且社会福利函数为凸函数时，可鲁棒实现的最优解具有极其简洁的形式：每个状态下实现完全协调——要么所有智能体都采取行动，要么都不行动。我们提出了一种构造性阈值规则：为每个状态计算一维评分，对状态进行排序，并选取单一阈值（至多对一个状态采用临界随机机制）。该规则是由可行性约束与序列服从约束刻画的线性规划（LP）的显式最优顶点。在疫苗接种与技术采纳两个领域的实证研究表明，我们提出的构造性策略与线性规划最优解一致，其计算复杂度为 $O(|Θ|\log|Θ|)$，并且避免了仅考虑服从约束的设计方案（此类方案假设设计者能够指定最优均衡）所预测的虚高社会福利。本研究结果为具有互补性的多智能体系统提供了一种通用、可扩展的鲁棒协调方案。