AI 中文总结
研究动态战略通信问题，发送方控制二元连续时间马尔可夫源更新时间，与接收方构成斯塔克尔伯格博弈。提出最优策略及分支定界算法，将解决方案扩展到多接收方，结果显示控制及时性可助发送方说服接收方并提升效用。
AI 中文摘要
我们研究了一个动态战略通信问题，其中发送方控制来自二元连续时间马尔可夫源的真实更新的时间。接收方在跟随发送方更新的零阶保持估计器和仅使用先验信息的默认估计器之间进行选择，旨在最大化加权正确估计效用。而发送方试图说服接收方估计状态为1，无论真实状态如何。这种不一致导致了一个斯塔克尔伯格博弈，发送方作为领导者，承诺与状态相关的泊松更新率，接收方作为跟随者，决定是否跟随发送方的消息。发送方在有条件强度预算和参与约束下最大化接收方估计等于1的长期平均时间。对于单个源，我们表明发送方的最优策略为不期望的状态0分配最小的更新强度，仅足以满足参与约束，其余预算分配给期望的状态1。对于具有异质最小状态0更新强度的多个源，我们开发了一种分支定界算法，通常避免穷举搜索。最后，我们将解决方案扩展到通过专用信道的多个接收方。我们的结果表明，仅控制及时性就能使发送方说服接收方并提高其效用。
英文摘要
We study a dynamic strategic communication problem in which a sender controls the timing of truthful updates from binary continuous-time Markov sources. The receiver chooses between a zero-order-hold estimator that follows the sender's updates and a prior-only default estimator, aiming to maximize a weighted correct-estimation utility. In contrast, the sender seeks to persuade the receiver to estimate the state as 1, regardless of the true state. This misalignment leads to a Stackelberg game in which the sender, as the leader, commits to state-dependent Poisson update rates, and the receiver, as the follower, decides whether to follow the sender's messages. The sender maximizes the long-term average time that the receiver's estimate equals 1, subject to a conditional intensity budget and a participation constraint (PC) ensuring that following the sender's messages does not degrade the receiver's average utility relative to its prior information. For a single source, we show that the sender's optimal policy allocates a minimum state-0 update intensity to the undesired state-0, just enough to satisfy the PC, and the remaining budget to the desired state-1. For multiple sources with heterogeneous minimum state-0 update intensities, we develop a branch-and-bound algorithm that typically avoids exhaustive search. Finally, we extend the solution to multiple receivers over dedicated channels. Our results show that controlling timeliness alone enables the sender to persuade the receiver and increase its utility.
CommentsThis paper is an extended journal version of our conference paper, which is available on arXiv as arXiv:2512.04679
