Sprite ignoring collison

Let me set up the situation first: I have 2 characters on the map that I have loaded into the game that move the exact same time. Suppose character 1 is at 1,0 and character 2 is at 0,1 and both want to move to 0,0. The collision detector that I learned from Tutorial RogueLike is allowing them to both move into the same space at the same time. Any Idea how to be able to test for this and stop it from happening. I have thought about giving them different time to move but unrealistic in my game as I could have thousands of characters moving around on a screen.