A Games-in-Games Paradigm for Strategic Hybrid Jump-Diffusions: Hamilton-Jacobi-Isaacs Hierarchy and Spectral Structure
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909972164509696 |
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| author | Pan, Yunian Zhu, Quanyan |
| author_facet | Pan, Yunian Zhu, Quanyan |
| contents | This paper develops a hierarchical games-in-games control architecture for hybrid stochastic systems governed by regime-switching jump-diffusions. We model the interplay between continuous state dynamics and discrete mode transitions as a bilevel differential game: an inner layer solves a robust stochastic control problem within each regime, while a strategic outer layer modulates the transition intensities of the underlying Markov chain. A Dynkin-based analysis yields a system of coupled Hamilton-Jacobi-Isaacs (HJI) equations. We prove that for the class of Linear-Quadratic games and Exponential-Affine games, this hierarchy admits tractable semi-closed form solutions via coupled matrix differential equations. We prove that for the class of Linear-Quadratic games and Exponential-Affine games, this hierarchy admits tractable semi-closed form solutions via coupled matrix differential equations. The framework is demonstrated through a case study on adversarial market microstructure, showing how the outer layer's strategic switching pre-emptively adjusts inventory spreads against latent regime risks, which leads to a hyper-alert equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18098 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Games-in-Games Paradigm for Strategic Hybrid Jump-Diffusions: Hamilton-Jacobi-Isaacs Hierarchy and Spectral Structure Pan, Yunian Zhu, Quanyan Systems and Control This paper develops a hierarchical games-in-games control architecture for hybrid stochastic systems governed by regime-switching jump-diffusions. We model the interplay between continuous state dynamics and discrete mode transitions as a bilevel differential game: an inner layer solves a robust stochastic control problem within each regime, while a strategic outer layer modulates the transition intensities of the underlying Markov chain. A Dynkin-based analysis yields a system of coupled Hamilton-Jacobi-Isaacs (HJI) equations. We prove that for the class of Linear-Quadratic games and Exponential-Affine games, this hierarchy admits tractable semi-closed form solutions via coupled matrix differential equations. We prove that for the class of Linear-Quadratic games and Exponential-Affine games, this hierarchy admits tractable semi-closed form solutions via coupled matrix differential equations. The framework is demonstrated through a case study on adversarial market microstructure, showing how the outer layer's strategic switching pre-emptively adjusts inventory spreads against latent regime risks, which leads to a hyper-alert equilibrium. |
| title | A Games-in-Games Paradigm for Strategic Hybrid Jump-Diffusions: Hamilton-Jacobi-Isaacs Hierarchy and Spectral Structure |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2512.18098 |