论文标题
减轻流行病的最佳激励措施：Stackelberg平均野外游戏方法
Optimal incentives to mitigate epidemics: a Stackelberg mean field game approach
论文作者
论文摘要
在大量人群中的流行病控制模型中，我们考虑了在有限状态空间上演变的主体和代理商的平均场所之间的平均野外游戏模型。代理商玩不合作的游戏，他们可以控制各州之间的过渡速率，以最大程度地减少个人成本。委托人可以通过激励措施来影响最终的纳什均衡，从而优化其自己的目标。我们使用概率方法分析了该游戏。然后，我们提出对SIR类型流行模型的应用，其中代理控制其相互作用速率，并且主是具有非药物干预措施的调节器。为了计算解决方案，我们提出了一种基于蒙特卡洛模拟和机器学习工具进行随机优化的创新数值方法。我们通过数字实验来结束，通过说明了两个模型中的代理和监管机构的最佳决策的影响：具有半阐释解决方案的基本SIR模型和具有更大状态空间的更复杂模型。
Motivated by models of epidemic control in large populations, we consider a Stackelberg mean field game model between a principal and a mean field of agents evolving on a finite state space. The agents play a non-cooperative game in which they can control their transition rates between states to minimize an individual cost. The principal can influence the resulting Nash equilibrium through incentives so as to optimize its own objective. We analyze this game using a probabilistic approach. We then propose an application to an epidemic model of SIR type in which the agents control their interaction rate and the principal is a regulator acting with non pharmaceutical interventions. To compute the solutions, we propose an innovative numerical approach based on Monte Carlo simulations and machine learning tools for stochastic optimization. We conclude with numerical experiments by illustrating the impact of the agents' and the regulator's optimal decisions in two models: a basic SIR model with semi-explicit solutions and a more complex model with a larger state space.
