Distributed games with jumps: An $α$-potential game approach
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866910133663039488 |
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| author | Guo, Xin Li, Xinyu Zhang, Yufei |
| author_facet | Guo, Xin Li, Xinyu Zhang, Yufei |
| contents | Motivated by game-theoretic models of crowd motion dynamics, this paper analyzes a broad class of distributed games with jump diffusions within the recently developed $α$-potential game framework. We demonstrate that analyzing the $α$-Nash equilibria reduces to solving a finite-dimensional control problem. Beyond the viscosity and verification characterizations for the general games, we examine explicitly and in detail how spatial population distributions and interaction rules influence the structure of $α$-Nash equilibria in these distributed settings.
For crowd motion network games, we show that $α= 0$ for all symmetric interaction networks, and or asymmetric networks. We quantify the precise polynomial and logarithmic decays of $α$ in terms of the number of players, the degree of the network, and the decay rate of interaction asymmetry. We also exploit the $α$-potential game framework to analyze an $N$-player portfolio selection game under a mean-variance criterion. We show that this portfolio game constitutes a potential game and explicitly construct its Nash equilibrium. Our analysis allows for heterogeneous preference parameters, going beyond the mean-field interactions considered in the existing game literature.
Our theoretical results are supported by numerical implementations using policy gradient-based algorithms, demonstrating the computational advantages of the $α$-potential game framework in computing Nash equilibria for general dynamic games. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_01929 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributed games with jumps: An $α$-potential game approach Guo, Xin Li, Xinyu Zhang, Yufei Optimization and Control Multiagent Systems Probability 91A06, 91A15, 91A14, 91A16 Motivated by game-theoretic models of crowd motion dynamics, this paper analyzes a broad class of distributed games with jump diffusions within the recently developed $α$-potential game framework. We demonstrate that analyzing the $α$-Nash equilibria reduces to solving a finite-dimensional control problem. Beyond the viscosity and verification characterizations for the general games, we examine explicitly and in detail how spatial population distributions and interaction rules influence the structure of $α$-Nash equilibria in these distributed settings. For crowd motion network games, we show that $α= 0$ for all symmetric interaction networks, and or asymmetric networks. We quantify the precise polynomial and logarithmic decays of $α$ in terms of the number of players, the degree of the network, and the decay rate of interaction asymmetry. We also exploit the $α$-potential game framework to analyze an $N$-player portfolio selection game under a mean-variance criterion. We show that this portfolio game constitutes a potential game and explicitly construct its Nash equilibrium. Our analysis allows for heterogeneous preference parameters, going beyond the mean-field interactions considered in the existing game literature. Our theoretical results are supported by numerical implementations using policy gradient-based algorithms, demonstrating the computational advantages of the $α$-potential game framework in computing Nash equilibria for general dynamic games. |
| title | Distributed games with jumps: An $α$-potential game approach |
| topic | Optimization and Control Multiagent Systems Probability 91A06, 91A15, 91A14, 91A16 |
| url | https://arxiv.org/abs/2508.01929 |