It's okay to start writing with no end in sight, but it is a very good idea to make decisions about your characters even if the results are ambiguous to the audience. I go to plays regularly and the weakest part of modern plays is inevitably the second act and the ending...to the point that I feel like walking out at intermission. Why? Because the authors spend a lot of time with their beginnings and the first act closing lines, and then they drift in the second act. Next weakest part is the character development because the writers are so busy being clever that they forget to develop the characters...thinking, I guess, that the actors will flesh out their creation, but I wouldn't depend on that as an idea. It takes a great actor to create a character out of nothing. I encourage you with all my heart to put as much thought and effort into the second act as the first. Remember, plays are written to be seen and heard by an audience. Novels are meant to be written for the reader. Plays have acts that are stops along the road. Novels are the road. Be very clear on whom you are writing for...I'd make that decision before I moved forward with the story because it will make all the difference in the world as to how your plotline reveals itself. Just a suggestions. Safe to ignore.