Strategic Information Transmission over Gossip Networks

2026-09-03

AI Summary

研究通过Stackelberg博弈和随机混合系统框架，解决在通信预算限制下策略发送者如何在完全连接的八卦网络中有效传递关于二元连续时间马尔可夫源的信息问题。

Abstract

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.

Problem

• gossip networks
• strategic information transmission
• communication budget
• Stackelberg game
• stochastic hybrid systems

Innovation

• Stackelberg game
• stochastic hybrid systems (SHS)
• communication budget
• gossip networks
• Markov source