Well-posedness and propagation of chaos for multi-agent models with strategies and diffusive effects
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908903737917440 |
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| author | Baldi, Alessandro Morandotti, Marco |
| author_facet | Baldi, Alessandro Morandotti, Marco |
| contents | A multi-agent model for individuals endowed with strategies and subject to diffusive effects is proposed. The microscopic state of each agent is described by a spatial position and a probability measure, interpreted as a mixed strategy, over a compact metric space. The evolution is governed by a non-local interaction mechanism and by stochastic effects acting on the spatial component of the state. The well-posedness of the multi-agent system and that of a certain McKean--Vlasov stochastic differential equation are proved. Eventually, a propagation of chaos result is obtained, which guarantees that the former model converges to the latter as the number of agents goes to infinity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_14058 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness and propagation of chaos for multi-agent models with strategies and diffusive effects Baldi, Alessandro Morandotti, Marco Analysis of PDEs Probability 34F05, 60K35, 93A16, 60H10 A multi-agent model for individuals endowed with strategies and subject to diffusive effects is proposed. The microscopic state of each agent is described by a spatial position and a probability measure, interpreted as a mixed strategy, over a compact metric space. The evolution is governed by a non-local interaction mechanism and by stochastic effects acting on the spatial component of the state. The well-posedness of the multi-agent system and that of a certain McKean--Vlasov stochastic differential equation are proved. Eventually, a propagation of chaos result is obtained, which guarantees that the former model converges to the latter as the number of agents goes to infinity. |
| title | Well-posedness and propagation of chaos for multi-agent models with strategies and diffusive effects |
| topic | Analysis of PDEs Probability 34F05, 60K35, 93A16, 60H10 |
| url | https://arxiv.org/abs/2507.14058 |