Consider the following game: Players 1 and 2 are partners in several group projects for a course. Three of these group projects, A, B and C, are due tomorrow. Both players have time to work on exactly one project tonight. Projects A and B can be completed by just one person, while C can only be completed if both partners work on it. The players cannot communicate with each other and must choose simultaneously which project each will work on. Projects A, B and C are worth 30, 20 and 50 points respectively. If a project is completed, both partners get the points associated with it. If a project is not completed, both players get 0 for it. If more than one project is completed, both players get the sum of the points associated with the completed projects. Players' payoffs are the total points they earn. (Do not need to include payoff matrix in your answer) a) Using the payoff matrix, find all pure strategy Nash equilibria in this game. Now suppose Players 1 and 2 can only choose to work on projects A or C. The rest of the game remains as before. b) Using the payoff matrix for the new game, Find all Nash equilibria in pure strategies. c) Are any of the equilibria you found in part b inadmissible? If so, which ones and why (1 sentence)