Dynamic-Programming-Game-Theory-2-Players-Game

Consider a 2 players game where 2 players are standing facing each other in distance A. The players approach each other by putting each foot exactly in front of the other while walking. During their approach they have the choice to make a horizontal step (so they approch each other by D) or to make a vertical step (so they approach each other by d). Consider the paramenters d and D are known and the same for both players. The winner is the player who will touch his opponent first.