Speaker: Massimo Fornasier , Technische Universität München
L. Ambrosio, M. Fornasier, M. Morandotti, and S. Savaré. Spatially Inhomogeneous Evolutionary Games, May 2018.
We present a mean-field model for a system of spatiallydistributed players interacting through an evolutionary game driven by areplicator dynamics. Strategies evolve by a replicator dynamics influenced bythe position and the interaction between different players and return afeedback on the velocity field guiding their motion.The description of the whole system is realized by an evolving probability measure Σ on an infinite dimensional state space (pairs (x,σ) of positionand distribution of strategies). We provide a Lagrangian and a Euleriandescription of the evolution, and we show their equivalence, together withexistence, uniqueness, and stability of the solution. As a byproduct of thestability result, we also present convergence of the finite agents model to ourmean-field formulation, when the number N of the players goes to infinity.