Forward-Looking Dynamic Persuasion for Pipeline Stochastic Bayesian Game: A Fixed-Point Alignment Principle

This paper studies a general-sum two-player pipeline stochastic game where each period is composed of two stages. The agents have uncertainty about the transition of the state which is characterized by a variable known as shock. The first stage is cognitive decision-making in which each agent selects one of multiple information sources (ISs) and then acquires information about the shock from his selected IS. In the second stage, each agent takes an action based on the information provided by his selected IS. There is a rational Bayesian persuader who controls one IS and aims to influence the agents' actions to induce her desired dynamic equilibria by solely crafting the information structure of her IS. We refer to such persuasion as forward-looking dynamic persuasion. We restrict attention to a direct persuasion in which the persuader incentivizes the agents to select her IS at the first stage and consider an equilibrium concept known as pipelined perfect Markov Bayesian equilibrium (PPME). We propose a novel design principle termed fixed-point alignment that captures the observation that the agents' strategic interactions in the second stage induce an indirect cognitive competition (i.e., IS selection) in the first stage and formulate the direct Bayesian persuasion in PPME as a constrained non-linear optimization problem. By decomposing the optimization problem into a two-stage local process, we then provide a class of verifiable necessary and sufficient condition referred to as local admissibility of the direct Bayesian persuasion in PPME. A case study is provided in which we obtain a myopic version of local admissibility, by solving a series of static problems which is homogeneous with respect to the state variable