Econ Papers Daily / 期刊论文
粗沟通中的说服
Persuasion with Coarse Communication
摘要
In many expert–decision maker settings, information is richer than the language used to convey it. Motivated by this communication friction, we study Bayesian persuasion when the sender is constrained to use k messages. We show that the sender’s value is given by a k -point analogue of concavification, which we call k -concavification. An optimal information structure can be chosen with affinely independent posterior support, allowing the problem to be reduced to a lower-dimensional persuasion problem and then solved by standard concavification. We derive a tight bound on the value of communication capacity that applies to general persuasion games: the gain from a $$(k+1)$$ ( k + 1 ) st message is at most $$2/(k-1)$$ 2 / ( k - 1 ) times the value attainable with k messages. Finally, we solve a class of belief-threshold games in which the receiver chooses between a safe default and several risky actions, the sender gets zero from the default and the same positive payoff from any risky action, and a risky action is taken only when the corresponding posterior probability exceeds a threshold. We characterize the optimal coarse information structure, derive comparative statics in the prior and the threshold, and extend the analysis to heterogeneous thresholds and heterogeneous sender values across risky actions.
中文摘要
摘要 在许多专家与决策者互动的场景中，信息本身比用于传递信息的语言更为丰富。受这种沟通摩擦的启发，我们研究了当发送者被限制使用k条消息时的贝叶斯说服问题。我们证明，发送者的价值由凹化概念的k点对应物给出，我们称之为k-凹化。最优信息结构可以选择具有仿射独立后验支撑的形式，从而将问题简化为低维说服问题，并通过标准凹化方法求解。我们推导了适用于一般说服博弈的沟通容量价值的紧界：第(k+1)条消息带来的增益最多为k条消息可实现价值的2/(k-1)倍。最后，我们求解了一类信念阈值博弈，其中接收者在安全默认选项与多个风险行动之间进行选择，发送者从默认选项中获得零收益，从任何风险行动中获得相同的正收益，且仅当相应的后验概率超过阈值时才采取风险行动。我们刻画了最优粗糙信息结构，推导了关于先验和阈值的比较静态分析，并将分析扩展至风险行动具有异质性阈值和异质性发送者价值的情形。