Well-posedness and propagation of chaos for multi-agent models with strategies and diffusive effects

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...

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Bibliographic Details
Main Authors Baldi, Alessandro, Morandotti, Marco
Format Journal Article
LanguageEnglish
Published 23.07.2025
Subjects
Mathematics - Analysis of PDEs
Mathematics - Probability
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Summary: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.
DOI:10.48550/arxiv.2507.14058