Hierarchical Bayesian Persuasion

We study a hierarchical Bayesian persuasion game with a sender, a receiver and several potential intermediaries, in the framework of Kamenica and Gentzkow (2011, AER). The sender must be persuasive through the hierarchy of intermediaries in order to reach the final receiver, whose action affects all players’ payoffs. We characterize the subgame perfect equilibria for the optimal persuasion strategy, and show that the persuasion game has multiple equilibria but a unique payoff outcome. Among the equilibria, two natural persuasion strategies on the hierarchy arise: persuading the intermediary who is immediately above one’s own position, and persuading the least persuadable individual in the hierarchy. As major extensions of the main model, we analyze scenarios in which intermediaries have private information, the endogenous reputation of intermediaries, and when intermediaries have an outside option. We also discuss as minor extensions, the endogenous choice of persuasion path, parallel persuasion, and costly persuasion. The results provide insights for settings where persuasion is prominent in a hierarchical structure, such as corporate management, higher education admissions, job promotion, and legal proceedings.