Spatially Inhomogeneous Evolutionary Games

We introduce and study a mean-field model for system of spatially distributed players interacting through an evolutionary game driven by replicator dynamics. Strategies evolve dynamics influenced the position interaction between different return feedback on velocity field guiding their motion. One main novelties our approach concerns description whole system, which can be represent-dimensional state space (pairs (x, ?) distribution strategies). provide Lagrangian Eulerian evolution, we prove equivalence, together with existence, uniqueness, stability solution. As byproduct result, also obtain convergence finite agents to formulation, when number N goes infinity, initial discrete positions strategies converge. To this aim develop some basic functional analytic tools deal continuity equations in Banach spaces that could independent interest. © 2021 Wiley Periodicals LLC.