论文标题
Hypergraphon平均野外游戏
Hypergraphon Mean Field Games
论文作者
论文摘要
我们提出了一种建模大规模多代理动力系统的方法，它允许使用平均野外游戏理论和超图形概念的相互作用，而不是对大量术的概念，这些概念是大型超透明剂的限制。据我们所知，我们的是HyperGraphs平均野外游戏的第一部作品。加上延伸到多层设置，我们获得了非线性，弱相互作用的动力学剂的大系统的限制描述。从理论方面来说，我们证明了由此产生的超图平均野外游戏的良好基础，显示了存在和近似NASH属性。在应用的一侧，我们扩展了数值并学习算法以计算超图平均磁场平衡。为了从经验上验证我们的方法，我们考虑了一个社会谣言传播模型，在该模型中，我们为代理人提供了将谣言传播到不知道的代理商的内在动机，以及一个流行病的控制问题。
We propose an approach to modelling large-scale multi-agent dynamical systems allowing interactions among more than just pairs of agents using the theory of mean field games and the notion of hypergraphons, which are obtained as limits of large hypergraphs. To the best of our knowledge, ours is the first work on mean field games on hypergraphs. Together with an extension to a multi-layer setup, we obtain limiting descriptions for large systems of non-linear, weakly-interacting dynamical agents. On the theoretical side, we prove the well-foundedness of the resulting hypergraphon mean field game, showing both existence and approximate Nash properties. On the applied side, we extend numerical and learning algorithms to compute the hypergraphon mean field equilibria. To verify our approach empirically, we consider a social rumor spreading model, where we give agents intrinsic motivation to spread rumors to unaware agents, and an epidemics control problem.
