On the Monotonicity and Rate of Convergence of the Markovian Persuasion Value

• 成果类型: Article; Early Access
• 署名作者: Shaiderman, Dimitry
• 署名单位: Hebrew University of Jerusalem
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2023.0296
• 发表日期: 2026-04-06
• 关键词: Markovian persuasion; repeated games with incomplete information on one side; Markov chains; discounted values; monotone trajectories; Rate Of Convergence; mixing times; repeated games; CHAIN GAMES; INFORMATION

摘要

We study a dynamic Bayesian persuasion model called Markovian persuasion, illustrated here with two players: the sender (he) and the receiver (she). In such a model, the belief of the receiver regarding the current state of a Markov chain (X-n)(n >= 1), over a finite state space K, is controlled through signals she obtains from a sender, who observes (X-n)(n >= 1) in real time. At each stage n >= 1, the receiver takes an action based on his current belief, which, together with the realized state of X-n, determines the n-th-stage payoff of the sender. The sender's goal in a Markovian persuasion game is to find a signaling policy that maximizes her expected delta-discounted sum of stage payoffs for a discount factor delta is an element of[0,1). We show that starting from any invariant distribution (X-n)(n >= 1), the trajectory of the delta-discounted value is monotone decreasing in delta. By combining this result with the opposite increasing monotone trajectories found in Lehrer and Shaiderman [Lehrer E, Shaiderman D (2025) Markovian persuasion with stochastic revelations. Games Econom. Behav. 154:411-439], we are able to derive an upper bound on the rate of convergence of the delta-discounted values (as delta -> 1-) in the case where (X-n)(n >= 1) is ergodic. The results for the Markovian persuasion model are then extended to the Markov chain games model of Renault (2006).