Tchoukouegno Ngnotchouye, Jean Medard.Joseph, Kristina.2018-06-142018-06-1420172017http://hdl.handle.net/10413/15307Master of Science in Applied Mathematics. University of KwaZulu-Natal Pietermaritzburg 2017.This dissertation deals with the study of non-cooperative di erential games with pure state constraints. We propose a rst order optimality result for the open-loop Nash and Stackelberg equilibriums solutions of an N-player di erential game with pure state constraints. A numerical method to solve for an open-loop Nash equilibrium is discussed. Numerical examples are included to illustrate this method.en-ZATheses - Mathematics and Computer Science Education.Stackelberg Equilibrium.Nash Equilibrium.Differential Games.N-player differential games.Thesis