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

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.

References in corpus (14)

• Generalized Wasserstein distance and its application to transport equations with source
• A consensus-based model for global optimization and its mean-field limit
• Invisible control of self-organizing agents leaving unknown environments
• Wealth distribution under the spread of infectious diseases
• Propagation of chaos: a review of models, methods and applications. II. Applications
• Instantaneous control of interacting particle systems in the mean-field limit
• Kinetic-controlled hydrodynamics for traffic models with driver-assist vehicles
• Model-based assessment of the impact of driver-assist vehicles using kinetic theory
• Consensus-Based Optimization Methods Converge Globally
• Continuification-based control of large multiagent systems in a ring
• Boltzmann-type equations for multi-agent systems with label switching
• Herding stochastic autonomous agents via local control rules and online global target selection strategies
• Kinetic description and macroscopic limit of swarming dynamics with continuous leader-follower transitions
• Mean-field optimal control for biological pattern formation