Abstract
It is argued that diffusion in biological and economical systems is better modelled by Cattaneo's equation where memory effects are included. Reaction diffusion equations using Cattaneo's system are derived for prisoner's dilemma (PD) and hawk-dove (HD) games. Nonlinear wave solutions are derived for them. As expected the asymptotic solution for the PD case is insufficient. Hence a cellular automata motivated by Cattaneo's system is used to show the existence of cooperation in the case of local game.