A Fast Algorithm for k-Memory Messaging Scheme Design in Dynamic Environments with Uncertainty

Abstract

We study the problem of designing the optimal k-memory messaging scheme in a dynamic environment. Specifically, a sender, who can perfectly observe the state of a dynamic environment but cannot take actions, aims to persuade an uninformed, far-sighted receiver to take actions to maximize the long-term utility of the sender, by sending messages. We focus on k-memory messaging schemes, i.e., at each time step, the sender's messaging scheme depends on information from the previous k steps. After receiving a message, the self-interested receiver derives a posterior belief and takes action. The immediate reward of each player can be unaligned, thus the sender needs to ensure persuasiveness when designing the messaging scheme. We first formulate this problem as a bi-linear program. Then we show that there are infinitely many non-trivial persuasive messaging schemes for any problem instance. Moreover, we show that when the sender uses a k-memory messaging scheme, the optimal strategy for the receiver is also a k-memory strategy. We propose a fast heuristic algorithm for this problem and show that it can be extended to the setting where the sender has threat ability. We experimentally evaluate our algorithm, comparing it with the solution obtained by the Gurobi solver, in terms of performance and running time, in both settings. Extensive experimental results show that our algorithm outperforms the solution in running time, yet achieves comparable performance.