Semi-Explicit Solution of Some Discrete-Time Mean-Field-Type Games with Higher-Order Costs
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| author | Barreiro-Gomez, Julian Duncan, Tyrone E. Pasik-Duncan, Bozenna Tembine, Hamidou |
| author_facet | Barreiro-Gomez, Julian Duncan, Tyrone E. Pasik-Duncan, Bozenna Tembine, Hamidou |
| contents | Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they often fail to capture critical non-linearities inherent in real-world systems. In this work, we present a unified framework for solving discrete-time game problems with higher-order state and strategy costs involving power-law terms. We derive semi-explicit expressions for equilibrium strategies, cost-to-go functions, and recursive coefficient dynamics across deterministic, stochastic, and multi-agent system settings by convex-completion techniques. The contributions include variance-aware solutions under additive and multiplicative noise, extensions to mean-field-type-dependent dynamics, and conditions that ensure the positivity of recursive coefficients. Our results provide a foundational methodology for analyzing non linear multi-agent systems under higher-order penalization, bridging classical game theory and mean-field-type game theory with modern computational tools for engineering applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04988 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semi-Explicit Solution of Some Discrete-Time Mean-Field-Type Games with Higher-Order Costs Barreiro-Gomez, Julian Duncan, Tyrone E. Pasik-Duncan, Bozenna Tembine, Hamidou Optimization and Control Systems and Control Traditional solvable game theory and mean-field-type game theory (risk-aware games) predominantly focus on quadratic costs due to their analytical tractability. Nevertheless, they often fail to capture critical non-linearities inherent in real-world systems. In this work, we present a unified framework for solving discrete-time game problems with higher-order state and strategy costs involving power-law terms. We derive semi-explicit expressions for equilibrium strategies, cost-to-go functions, and recursive coefficient dynamics across deterministic, stochastic, and multi-agent system settings by convex-completion techniques. The contributions include variance-aware solutions under additive and multiplicative noise, extensions to mean-field-type-dependent dynamics, and conditions that ensure the positivity of recursive coefficients. Our results provide a foundational methodology for analyzing non linear multi-agent systems under higher-order penalization, bridging classical game theory and mean-field-type game theory with modern computational tools for engineering applications. |
| title | Semi-Explicit Solution of Some Discrete-Time Mean-Field-Type Games with Higher-Order Costs |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2505.04988 |