In many real-world large-scale decision problems, self-interested agents have individual dynamics and optimize their own long-term payoffs. Important examples include the competitive access to shared resources (e.g., roads, energy, or bandwidth) but also non-engineering domains like epidemic propagation and control. These problems are natural to model as mean-field games. However, existing mathematical formulations of mean field games have had limited applicability in practice, since they require solving non-standard initial-terminal-value problems that are tractable only in limited special cases. In this letter, we propose a novel formulation, along with computational tools, for a practically relevant class of Dynamic Population Games (DPGs), which correspond to discrete-time, finite-state-and-action, stationary mean-field games. Our main contribution is a mathematical reduction of Stationary Nash Equilibria (SNE) in DPGs to standard Nash Equilibria (NE) in static population games. This reduction is leveraged to guarantee the existence of a SNE, develop an evolutionary dynamics-based SNE computation algorithm, and derive simple conditions that guarantee stability and uniqueness of the SNE. Additionally, DPGs enable us to tractably incorporate multiple agent types, which is of particular importance to assess fairness concerns in resource allocation problems. We demonstrate our results by computing the SNE in two complex application examples: fair resource allocation with heterogeneous agents and control of epidemic propagation. Open source software for SNE computation: https://gitlab.ethz.ch/elokdae/dynamic-population-games

翻译：在许多现实世界的大规模决策问题中，自利主体具有个体动态性并优化其长期收益。重要例子包括对共享资源（如道路、能源或带宽）的竞争性访问，以及流行病传播与控制等非工程领域。这些问题自然适合建模为平均场博弈。然而，现有平均场博弈的数学公式在实际应用中适用性有限，因为它们需要求解非标准的初终值问题，而这仅在有限的特殊情况下才可处理。本文针对一类实际相关的动态群体博弈（DPGs）提出了一种新颖的公式及计算工具，该博弈对应于离散时间、有限状态与动作的平稳平均场博弈。我们的主要贡献是将DPG中的平稳纳什均衡（SNE）数学简化为静态群体博弈中的标准纳什均衡（NE）。利用这一简化，我们保证了SNE的存在性，开发了一种基于演化动力学的SNE计算算法，并推导出了保证SNE稳定性和唯一性的简单条件。此外，DPG使我们能够可处理地纳入多种主体类型，这在评估资源分配问题中的公平性关注时尤为重要。我们通过计算两个复杂应用示例中的SNE来展示结果：异质主体下的公平资源分配和流行病传播的控制。SNE计算的开源软件：https://gitlab.ethz.ch/elokdae/dynamic-population-games