Give typed solution

24. Black Friday, the day after Thanksgiving that has become an unofficial shopping holiday in recent decades, seems to get bigger and bigger every year. And stores have been gradually opening earlier and earlier every year. Originally, "Black Friday" started on Friday morning at the normal store opening times. Then stores started opening earlier than usual that day. Then they started opening at midnight. Then they began to open even before midnight, on Thanksgiving Day itself. Everyone seems to hate the way that Black Friday is "eating up" Thanksgiving, but no one seems to be able to stop it. Why? Let's use Game Theory to make sense of this. Imagine you are the manager of a big retail store, and you have a choice between opening at the same time as last year on Black Friday, or an hour earlier. You know that a nearby rival store is facing the same choice. If the two stores open at the same time, they will make the same amount of money. But if one store opens earlier than the other, that store that opens early will take away 25% of the other store's customers. Explain what is going to be the Nash Equilibrium in this situation, and the decisions that lead us to that Nash Equilibrium.25. In the 2008 movie The Dark Knight, there is a point at which the main villain (the Joker) rigs two ferry boats with explosives, places the detonator for each one in the other boat, and then shuts off their engines in the middle of the river. So the passengers on each boat are trapped there, and they have the ability to destroy the other boat. The Joker says that if one boat pulls the trigger, he will let that boat go free. So the people on each boat are given an incentive to destroy the other boat before the others can do the same to them (and there's a possibility that they might both pull the trigger at the same time). However, the passengers on both boats also have hope of being rescued by Batman if they wait long enough. This is a job for Game Theory! Explain the "game" that the Joker was trying to play here (it's one of the games covered in our Game Theory chapter). Then, use Game Theory to show what we would expect to happen in this situation, if all the people involved were rational and self-interested. In the movie, the passengers on both boats chose not to pull the trigger (and of course everyone was rescued by Batman). What could motivate such a choice?