研究有外部性的博弈中，如何设计信号策略让多方参与者行为协同。
Bayesian Persuasion with Externalities: Exploiting Agent Types
- 将代理人按类型分组，利用类型同质性设计信号机制。
- 在固定偏离人数上限时，可多项式时间求解最优信号策略。
- 适用于多智能体协调、信息传递等场景，适合机制设计研究者。
我们研究带有外部性的贝叶斯劝说问题。在此模型中，主体向多个代理人发送信号以告知世界状态；同时，由于代理人效用存在外部性，主体也充当相关性装置，协调代理人的行动。考虑代理人被划分为少量类型的情形：同一类型的代理人具有相同的效用函数，并在他人及主体的效用函数中受到公平对待。我们研究了在三种不同信号通道（公开、私密、半私密）下，主体计算最优信号策略的问题。主要结果包括最优信号策略的揭示原理型刻画、线性规划公式化，以及优化问题的可解性分析。研究表明，当最大偏离代理人数量被常数限制时，基于线性规划的公式可在多项式时间内求出最优策略；否则，问题为NP难。
原文摘要 · Abstract (English)
We study a Bayesian persuasion problem with externalities. In this model, a principal sends signals to inform multiple agents about the state of the world. Simultaneously, due to the existence of externalities in the agents' utilities, the principal also acts as a correlation device to correlate the agents' actions. We consider the setting where the agents are categorized into a small number of types. Agents of the same type share identical utility functions and are treated equitably in the utility functions of both other agents and the principal. We study the problem of computing optimal signaling strategies for the principal, under three different types of signaling channels: public, private, and semi-private. Our results include revelation-principle-style characterizations of optimal signaling strategies, linear programming formulations, and analysis of in/tractability of the optimization problems. It is demonstrated that when the maximum number of deviating agents is bounded by a constant, our LP-based formulations compute optimal signaling strategies in polynomial time. Otherwise, the problems are NP-hard.
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