发表机构
TOBB University of Economics and Technology; Bilkent University; Queen’s University（托卜经济与技术大学; 比尔肯特大学; 女王大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文刻画了信号博弈中均衡结果的条件，证明在特定收益结构下随机化策略可提升发送者收益，并给出算法及统一结论。
AI 中文摘要
在发送者和接收者具有不一致标准的信号博弈中，均衡行为可能导致完全揭示、量化或随机化的策略。值得注意的是，第一种情况出现在统计决策理论和经典通信理论问题中，涉及完全对齐的传感器和接收者；第二种情况出现在纳什理论的同时信号博弈中；最后一种情况可能出现在斯塔克尔伯格型（领导者-跟随者）贝叶斯信号博弈中。本文研究了涉及试图估计源的接收者的贝叶斯说服问题。我们表明，对于某些收益结构，均衡解使得源观测以非零概率映射到不同的消息。更具体地，我们完全刻画了在涉及有限基数的一般源的贝叶斯说服问题中发送者需要随机化的条件。特别地，无论确定性策略限制下的均衡解是完全揭示、量化还是无信息，在本文刻画的某些条件下，存在一种随机化发送者策略能够提高发送者的收益。此外，我们提供了一种算法程序来获得贝叶斯说服解，该算法比较有限多个后验概率组合的收益。我们还考虑了完全对齐和完全错位的收益结构，其中解分别涉及完全揭示的发送者和无信息的发送者。然后，我们通过证明如果发送者关于后验分布的期望收益是连续的，则均衡解涉及完全揭示的发送者或无信息的发送者，来统一这些结果。
英文摘要
In signaling games where a sender and a receiver have misaligned criteria, equilibrium behavior may lead to fully revealing, quantized, or randomized policies. Notably, the first arises in statistical decision theory and classical communication theoretic problems involving a fully aligned sensor and receiver, the second arises in Nash theoretic simultaneous signaling games, and the last may appear in Stackelberg type (leader-follower) Bayesian signaling games. In this paper, we investigate the Bayesian persuasion problem involving a receiver that tries to estimate the source. We show that for certain payoff structures, the equilibrium solution is such that a source observation is mapped to distinct messages with nonzero probabilities. More specifically, we completely characterize conditions under which the sender requires randomization for the Bayesian persuasion problem involving general sources with finite cardinality. In particular, regardless of whether the equilibrium solution under a deterministic policy restriction is fully revealing, quantized or noninformative, there exists a randomized sender policy that improves the sender's payoff under certain conditions characterized in the paper. Moreover, we provide an algorithmic procedure to obtain the Bayesian persuasion solution, where the algorithm compares the payoffs with finitely many posterior probability combinations. We also consider fully aligned and completely misaligned payoff structures, where the solutions respectively involve a fully revealing sender and a noninformative sender. Then, we unify these results by proving that if the sender's expected payoff with respect to posterior distributions is continuous, then the equilibrium solution involves either a fully revealing sender or a noninformative sender.
Comments18 pages and 4 figures
