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. 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. We provide two examples of applications: 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，自利个体具有各自的动态特性并优化其自身长期收益。重要实例包括对共享资源（如道路、能源或带宽）的竞争性访问，以及非工程领域如流行病传播与控制。这些问题自然地适合建模为平均场博弈。现有平均场博弈的数学表述在实际应用中存在局限性，因为它们需要求解非标准的初值-终值问题，而这些问题仅在有限的特殊情况下可处理。本文提出了一种新颖的表述形式及计算工具，针对一类具有实际意义的动态人口博弈，该类博弈对应于离散时间、有限状态与动作的稳态平均场博弈。我们的主要贡献在于将DPG中的稳态纳什均衡数学归约为静态人口博弈中的标准纳什均衡。利用这一归约，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，并推导了保证SNE稳定性与唯一性的简明条件。我们提供了两个应用实例：异构个体的公平资源分配与流行病传播控制。SNE计算的开源软件地址：https://gitlab.ethz.ch/elokdae/dynamic-population-games