The literature on strategic communication originated with the influential cheap talk model, which precedes the Bayesian persuasion model by three decades. This model describes an interaction between two agents: sender and receiver. The sender knows some state of the world which the receiver does not know, and tries to influence the receiver's action by communicating a cheap talk message to the receiver. This paper initiates the algorithmic study of cheap talk in a finite environment (i.e., a finite number of states and receiver's possible actions). We first prove that approximating the sender-optimal or the welfare-maximizing cheap talk equilibrium up to a certain additive constant or multiplicative factor is NP-hard. Fortunately, we identify three naturally-restricted cases that admit efficient algorithms for finding a sender-optimal equilibrium. These include a state-independent sender's utility structure, a constant number of states or a receiver having only two actions.

翻译：战略沟通文献源于具有影响力的廉价交谈模型，该模型比贝叶斯说服模型早三十年。该模型描述了发送者与接收者两个智能体之间的交互：发送者知晓接收者未知的某种世界状态，并试图通过向接收者传递廉价交谈信息来影响其行动。本文在有限环境（即有限数量的状态和接收者可能采取的行动）中开启了廉价交谈的算法研究。我们首先证明，在加性常数或乘性因子范围内逼近发送者最优或福利最大化的廉价交谈均衡是NP难的。幸运的是，我们识别出三种自然受限情形，它们存在高效算法来寻找发送者最优均衡，包括：发送者效用函数与状态无关、状态数量为常数、以及接收者仅有两个行动。