Published Paper

Inserted: 20 jul 2025
Last Updated: 27 mar 2026

Journal: Journal of Differential Equations
Volume: 466
Pages: article no. 114329
Year: 2026
Doi: 10.1016/j.jde.2026.114329

Abstract:

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.

Keywords: mean-field limit, Multi-agent systems, propagation of chaos, stochastic differential equations, McKean-Vlasov equation

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