Stochastic Games on Large Sparse Graphs
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866914351692120064 |
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| author | Neuman, Eyal Tuschmann, Sturmius |
| author_facet | Neuman, Eyal Tuschmann, Sturmius |
| contents | We introduce a framework for stochastic games on large sparse graphs, covering continuous-time and discrete-time dynamic games as well as static games. Players are indexed by the vertices of simple, locally finite graphs, allowing both finite and countably infinite populations, with asymptotics described through local weak convergence of marked graphs. The framework allows path-dependent utility functionals that may be heterogeneous across players. Under a contraction condition, we prove existence and uniqueness of Nash equilibria and establish exponential decay of correlations with graph distance. We further show that global equilibria can be approximated by truncated local games, and can even be reconstructed exactly on subgraphs given information on their boundary. Finally, we prove convergence of Nash equilibria along locally weakly convergent graph sequences, including sequences sampled from hyperfinite unimodular random graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15557 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stochastic Games on Large Sparse Graphs Neuman, Eyal Tuschmann, Sturmius Optimization and Control 91A07, 91A15, 91A43, 93E20 We introduce a framework for stochastic games on large sparse graphs, covering continuous-time and discrete-time dynamic games as well as static games. Players are indexed by the vertices of simple, locally finite graphs, allowing both finite and countably infinite populations, with asymptotics described through local weak convergence of marked graphs. The framework allows path-dependent utility functionals that may be heterogeneous across players. Under a contraction condition, we prove existence and uniqueness of Nash equilibria and establish exponential decay of correlations with graph distance. We further show that global equilibria can be approximated by truncated local games, and can even be reconstructed exactly on subgraphs given information on their boundary. Finally, we prove convergence of Nash equilibria along locally weakly convergent graph sequences, including sequences sampled from hyperfinite unimodular random graphs. |
| title | Stochastic Games on Large Sparse Graphs |
| topic | Optimization and Control 91A07, 91A15, 91A43, 93E20 |
| url | https://arxiv.org/abs/2602.15557 |