System-Theoretic Analysis of Dynamic Generalized Nash Equilibria -- Turnpikes and Dissipativity
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| Format: | Preprint |
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2025
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| _version_ | 1866911592610791424 |
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| author | Hall, Sophie Dörfler, Florian Faulwasser, Timm |
| author_facet | Hall, Sophie Dörfler, Florian Faulwasser, Timm |
| contents | Generalized Nash equilibria are used in multi-agent control applications to model strategic interactions between agents that are coupled in the cost, dynamics, and constraints, and provide the foundations for game-theoretic MPC (Receding Horizon Games). We study properties of finite-horizon dynamic GNE trajectories from a system-theoretic perspective. We show how strict dissipativity generates the turnpike phenomenon in GNE solutions. Moreover, we establish a converse turnpike result, i.e., the implication from turnpike to strict dissipativity. We derive conditions under which the steady-state GNE is the optimal operating point and, using a game value function, we give a local characterization of the geometry of storage functions. Finally, we design linear terminal penalties that ensure dynamic GNE trajectories applied in open-loop converge to and remain at the steady-state GNE. These connections provide the foundation for future system-theoretic analysis of GNEs similar to those existing in optimal control as well as for recursive feasibility and closed-loop stability results of game-theoretic MPC. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_21556 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | System-Theoretic Analysis of Dynamic Generalized Nash Equilibria -- Turnpikes and Dissipativity Hall, Sophie Dörfler, Florian Faulwasser, Timm Systems and Control Generalized Nash equilibria are used in multi-agent control applications to model strategic interactions between agents that are coupled in the cost, dynamics, and constraints, and provide the foundations for game-theoretic MPC (Receding Horizon Games). We study properties of finite-horizon dynamic GNE trajectories from a system-theoretic perspective. We show how strict dissipativity generates the turnpike phenomenon in GNE solutions. Moreover, we establish a converse turnpike result, i.e., the implication from turnpike to strict dissipativity. We derive conditions under which the steady-state GNE is the optimal operating point and, using a game value function, we give a local characterization of the geometry of storage functions. Finally, we design linear terminal penalties that ensure dynamic GNE trajectories applied in open-loop converge to and remain at the steady-state GNE. These connections provide the foundation for future system-theoretic analysis of GNEs similar to those existing in optimal control as well as for recursive feasibility and closed-loop stability results of game-theoretic MPC. |
| title | System-Theoretic Analysis of Dynamic Generalized Nash Equilibria -- Turnpikes and Dissipativity |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2510.21556 |