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Dynamic Population Games: A Tractable Intersection of Mean-Field Games and Population Games

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  • Ezzat Elokda
  • Saverio Bolognani
  • Andrea Censi
  • Florian Dorfler
  • Emilio Frazzoli

Abstract

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

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  • Ezzat Elokda & Saverio Bolognani & Andrea Censi & Florian Dorfler & Emilio Frazzoli, 2021. "Dynamic Population Games: A Tractable Intersection of Mean-Field Games and Population Games," Papers 2104.14662, arXiv.org, revised Jun 2024.
    • Handle: RePEc:arx:papers:2104.14662
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