Dynamic Population Games: A Tractable Intersection of Mean-Field Games and Population Games
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arXiv
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| Format: | Preprint |
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2021
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| author | Elokda, Ezzat Bolognani, Saverio Censi, Andrea Dörfler, Florian Frazzoli, Emilio |
| author_facet | Elokda, Ezzat Bolognani, Saverio Censi, Andrea Dörfler, Florian Frazzoli, Emilio |
| contents | 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 |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2104_14662 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Dynamic Population Games: A Tractable Intersection of Mean-Field Games and Population Games Elokda, Ezzat Bolognani, Saverio Censi, Andrea Dörfler, Florian Frazzoli, Emilio Optimization and Control Computer Science and Game Theory Systems and Control Theoretical Economics 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 |
| title | Dynamic Population Games: A Tractable Intersection of Mean-Field Games and Population Games |
| topic | Optimization and Control Computer Science and Game Theory Systems and Control Theoretical Economics |
| url | https://arxiv.org/abs/2104.14662 |