Please help me with this

L7. [22 marks] Allen and John are roommates who study at the UofT. They need to choose a room to do their homework inliving room or their own bedroom. Assume that they need to make this choice at the same time. They both prefer to use the living room rather than their bedroom to do their homework, but Allen likes working in the living-room more than John does. They recently had a big fight and are trying to avoid being in the same room. If they're in the same room, they will have a really bad fight again. Fighting makes them both very unhappy. a. [10 marks] Create a payoff matrix consistent with the story in the question. Briefly explain how you generate these numbers. While the actual numbers are not important, they must match the story. b. [6 marks] Does any roommate have a dominant strategy? Clearly explain your answer. 0. [6 marks] Identify the Nash Equilibrium (or Equilibria) in this game, ifany. Clearly explain your