动态高斯信号博弈中均衡策略的结构
On the Structure of Equilibrium Strategies in Dynamic Gaussian Signaling Games
AI总结：
本文研究动态高斯信号博弈中均衡策略的结构，分析了在多阶段设置下纯策略Stackelberg均衡的存在性依赖于问题参数，揭示了信息利用与披露之间的权衡。
摘要：
本文分析了一个有限时间动态信号博弈，该博弈受到经济学中著名的战略信息传递问题的启发。数学模型涉及两个智能体之间的信息传递，发送方观察到两个高斯过程，即状态和偏差，而接收方根据发送方传递的消息采取行动。玩家的二次瞬时成本作为状态、偏差和行动变量的函数。我们的重点是Stackelberg均衡，这对应于经济学中的信息披露和贝叶斯说服问题。先前的工作解决了静态博弈，并展示了Stackelberg均衡通过状态和偏差变量的线性策略实现。本文的重点是动态（多阶段）设置，其中我们证明了在纯策略集合中Stackelberg均衡存在的依赖性在于问题参数。令人惊讶的是，对于大多数问题参数，纯线性策略无法实现Stackelberg均衡，这表明了在利用和揭示信息之间存在权衡，这一权衡也出现在其他非对称信息博弈中。
英文摘要：
This paper analyzes a finite horizon dynamic signaling game motivated by the well-known strategic information transmission problems in economics. The mathematical model involves information transmission between two agents, a sender who observes two Gaussian processes, state and bias, and a receiver who takes an action based on the received message from the sender. The players incur quadratic instantaneous costs as functions of the state, bias and action variables. Our particular focus is on the Stackelberg equilibrium, which corresponds to information disclosure and Bayesian persuasion problems in economics. Prior work solved the static game, and showed that the Stackelberg equilibrium is achieved by pure strategies that are linear functions of the state and the bias variables. The main focus of this work is on the dynamic (multi-stage) setting, where we show that the existence of a pure strategy Stackelberg equilibrium, within the set of linear strategies, depends on the problem parameters. Surprisingly, for most problem parameters, a pure linear strategy does not achieve the Stackelberg equilibrium which implies the existence of a trade-off between exploiting and revealing information, which was also encountered in several other asymmetric information games.
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