八卦网络上的策略性信息传输

中文摘要 AI 辅助

我们考虑一个由 $n$ 个节点组成的全连接八卦网络，这些节点通过一个策略性发送者跟踪一个二进制的连续时间马尔可夫源，该发送者在通信预算下以依赖于源状态的速率传输更新。接收者通过八卦交换数据包，并决定是否跟随发送者。我们将这种交互建模为 Stackelberg 博弈，并通过随机混合系统（SHS）框架进行分析。我们证明，在每一个内部最优解处，发送者的预算约束都是紧的，从而将其问题简化为在预算线上的一维搜索。当发送者以较高速率推送其偏好状态时，接收者以最高可用速率进行八卦。八卦本身没有方向性，它对抗发送者策略中的不对称性，而不是强化这种不对称性。我们证明了一个乐观的 Stackelberg 均衡的存在性，并且当该线策略半部分上的某个策略在八卦上限处可行时，该均衡是唯一的且被显式刻画。蒙特卡洛模拟与分析递归结果一致。

英文摘要

We consider a fully connected gossip network of $n$ nodes that track a binary continuous-time Markov source through a strategic sender transmitting updates under a communication budget at a rate that depends on the source state. The receivers exchange packets through gossip and decide whether to follow the sender. We model this interaction as a Stackelberg game and analyze it through a stochastic hybrid systems (SHS) framework. We prove that the sender's budget constraint binds at every interior optimum, reducing its problem to a one-dimensional search on the budget line. When the sender pushes its preferred state at the higher rate, the receivers gossip at the highest available rate. Gossip has no direction of its own and works against the asymmetry in the sender's policy rather than reinforcing it. We prove that an optimistic Stackelberg equilibrium exists, and that it is unique and explicitly characterized whenever a policy on the strategic half of that line is feasible at the gossip cap. Monte Carlo simulations agree with the analytical recursion.

发表机构

• Bilkent University（比尔肯特大学）

机构由 AI 辅助整理，请以论文原文为准。