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

TL;DR

This paper introduces a multi-agent model with strategies and diffusive effects, proving well-posedness and demonstrating that as the number of agents increases, the system converges to a McKean--Vlasov equation, establishing a propagation of chaos.

Contribution

It provides the first rigorous proof of well-posedness and propagation of chaos for multi-agent systems with strategy-based states and diffusive dynamics.

Findings

Proved well-posedness of the multi-agent model.

Established convergence to McKean--Vlasov equation as agents increase.

Demonstrated propagation of chaos in the system.

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.