A multi-step Lagrangian scheme for spatially inhomogeneous evolutionary games

Abstract A multi-step Lagrangian scheme at discrete times is proposed for the approximation of a nonlinear continuity equation arising as mean-field limit spatially inhomogeneous evolutionary games, describing evolution system distributed agents with strategies, or labels, whose payoff depends also on current position agents. The Lagrangian, it traces and labels along characteristics, scheme, develops following two stages: First, distribution strategies updated according to best performance criterion, then, this used by evolve their position. general convergence result provided in space probability measures. In special cases replicator-type systems reversible Markov chains, variants where explicit step replaced an implicit one, are considered results provided.