More Information is Not Always Better: Connections between Zero-Sum Local Nash Equilibria in Feedback and Open-Loop Information Patterns
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912283351842816 |
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| author | Gupta, Kushagra Allen, Ross Fridovich-Keil, David Topcu, Ufuk |
| author_facet | Gupta, Kushagra Allen, Ross Fridovich-Keil, David Topcu, Ufuk |
| contents | Non-cooperative dynamic game theory provides a principled approach to modeling sequential decision-making among multiple noncommunicative agents. A key focus has been on finding Nash equilibria in two-agent zero-sum dynamic games under various information structures. A well-known result states that in linear-quadratic games, unique Nash equilibria under feedback and open-loop information structures yield identical trajectories. Motivated by two key perspectives -- (i) many real-world problems extend beyond linear-quadratic settings and lack unique equilibria, making only local Nash equilibria computable, and (ii) local open-loop Nash equilibria (OLNE) are easier to compute than local feedback Nash equilibria (FBNE) -- it is natural to ask whether a similar result holds for local equilibria in zero-sum games. To this end, we establish that for a broad class of zero-sum games with potentially nonconvex-nonconcave objectives and nonlinear dynamics: (i) the state/control trajectory of a local FBNE satisfies local OLNE first-order optimality conditions, and vice versa, (ii) a local FBNE trajectory satisfies local OLNE second-order necessary conditions, (iii) a local FBNE trajectory satisfying feedback sufficiency conditions also constitutes a local OLNE, and (iv) with additional hard constraints on agents' actuations, a local FBNE where strict complementarity holds also satisfies local OLNE first-order optimality conditions, and vice versa. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15486 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | More Information is Not Always Better: Connections between Zero-Sum Local Nash Equilibria in Feedback and Open-Loop Information Patterns Gupta, Kushagra Allen, Ross Fridovich-Keil, David Topcu, Ufuk Computer Science and Game Theory Systems and Control Non-cooperative dynamic game theory provides a principled approach to modeling sequential decision-making among multiple noncommunicative agents. A key focus has been on finding Nash equilibria in two-agent zero-sum dynamic games under various information structures. A well-known result states that in linear-quadratic games, unique Nash equilibria under feedback and open-loop information structures yield identical trajectories. Motivated by two key perspectives -- (i) many real-world problems extend beyond linear-quadratic settings and lack unique equilibria, making only local Nash equilibria computable, and (ii) local open-loop Nash equilibria (OLNE) are easier to compute than local feedback Nash equilibria (FBNE) -- it is natural to ask whether a similar result holds for local equilibria in zero-sum games. To this end, we establish that for a broad class of zero-sum games with potentially nonconvex-nonconcave objectives and nonlinear dynamics: (i) the state/control trajectory of a local FBNE satisfies local OLNE first-order optimality conditions, and vice versa, (ii) a local FBNE trajectory satisfies local OLNE second-order necessary conditions, (iii) a local FBNE trajectory satisfying feedback sufficiency conditions also constitutes a local OLNE, and (iv) with additional hard constraints on agents' actuations, a local FBNE where strict complementarity holds also satisfies local OLNE first-order optimality conditions, and vice versa. |
| title | More Information is Not Always Better: Connections between Zero-Sum Local Nash Equilibria in Feedback and Open-Loop Information Patterns |
| topic | Computer Science and Game Theory Systems and Control |
| url | https://arxiv.org/abs/2503.15486 |