Hello it is related to Economics Game Theory Assignments. Kindly answer it asap

6. (24 points) Suppose that Joohyun and Sarah know that, at the start of the fall semester, they will each be randomly assigned to one of three offices in three different floors (floors 6, 7, and 8) of the Sewell Social Sciences building. They will not be assigned to the same floor. During the summer break, they are independently trying to decide whether they should suggest to the other to eat lunch together during the fall semester. If either Joohyun or Sarah suggests eating lunch together, the other person will accept the suggestion. Their rules of where they would eat lunch are as follows: If either of them is assigned an office in the 7th floor, they will meet in the Ph.D. student lounge on the 7th floor, and if neither of them is assigned the 7th floor, they will eat lunch in the office of the person whose office is on the 8th floor. If they don't eat lunch together, each person gets a utility of zero. Each gains 1 unit of utility if they do eat lunch together. However, both Joohyun and Sarah dislike moving between stairs carrying lunch and lose one unit of utility for every floor away from their floor that they have to go. Eating on the 7th floor together gives them each an additional utility of 2 because the lounge is so luxurious. (a) Formulate this game as a Bayesian game. . Hint 1: Construct the set of states so that it includes the case of both being on the same floor. Account for the fact that they cannot be assigned to the same floor through beliefs. . Hint 2: When drawing the payoff matrix, you may abstract away from which player is the row/column player and simply state the floor of the player. (b) Make tables with Sarah's expected payoffs for her action as entries. You should have one table for each possible floor that Sarah can be assigned. Put Sarah's strategies on the rows and Joohyun's strategies on the columns. You can simplify Joohyun's strategies in the tables by using the fact that the probability of Joohyun and Sarah being in the same floor is zero, and therefore the payoffs are unaffected by Joohyun's strategy in the states when they are on the same floor. (c) Evaluate whether (NEE, NEN) is a Bayesian Nash equilibrium. Ex- plain your work using the tables you have in (b). (d) Find at least four Bayesian Nash equilibria in this game in pure strategies. Verify that each strategy profile is indeed a BNE