This research note is organized with respect to a novel approach to solving
problems related to the spread of fake news and effective fact-checking.
Focusing on the least-cost routing problem, the discussion is organized with
respect to the use of Metzler functions and Metzler matrices to model the
dynamics of information propagation among news providers. With this approach,
we designed a strategy to minimize the spread of fake news, which is
detrimental to informational health, while at the same time maximizing the
spread of credible information. In particular, through the punitive dominance
problem and the maximum compensation problem, we developed and examined a path
to reassess the incentives of news providers to act and to analyze their impact
on the equilibrium of the information market. By applying the concept of
entanglement to the context of information propagation, we shed light on the
complexity of interactions among news providers and contribute to the
formulation of more effective information management strategies. This study
provides new theoretical and practical insights into issues related to fake
news and fact-checking, and will be examined against improving informational
health and public digital health.

针对假新闻的传播和有效事实核查问题，本研究借助 Metzler 函数和 Metzler 矩阵对新闻提供者之间信息传播动态进行建模，设计了一种策略来最小化有害的假新闻传播，同时最大化可信信息的传播。通过惩罚性支配问题和最大补偿问题，重新评估新闻提供者的激励并分析其对信息市场均衡的影响。通过将信息传播的纠缠概念应用于实际情境，揭示了新闻提供者之间相互作用的复杂性，并为制定更有效的信息管理策略提供了新的理论和实践见解。该研究旨在提高信息健康和公共数字健康。

纠结：平衡惩罚和补偿，基于重复困境博弈的事实检查中的最大赔偿问题分析，绕过和最小成本路径，虚假新闻与弱华莱士定律案例

Entanglement: Balancing Punishment and Compensation, Repeated Dilemma  Game-Theoretic Analysis of Maximum Compensation Problem for Bypass and Least  Cost Paths in Fact-Checking, Case of Fake News with Weak Wallace's Law