Question 2: You (player A) and your roommate (player B) are playing rock-paper-scissors to determine who has to clean the dormitory. The game works as follows: On the count of three, each of you must display either rock (fist), paper (open hand), or scissors (two fingers). Paper wins against Rock, Rock wins against Scissors, and Scissors wins against Paper. If you and your roommate both choose the same thing, it is a tie. Write the actions and payoffs for this one-shot game in the table below as (your payoff, roommate's payoff), where the winner gets +3, the loser gets 1. If it is a tie, both sides get 0 . A. Does there exist any pure strategy Nash equilibrium if you and your roommate are self-interested? If does, write down all the pure strategy Nash equilibria. B. Suppose you have reason to believe that Rock is the salient choice (many people make a fist while counting to three), and thus will be chosen (with certainty, for simplicity) by a totally non-strategic person. The outcome is that you chose scissors, and your roommate chose paper. According to a Level-k analysis, what (the lowest possible) Level are you? What (the lowest possible) Level is your roommate? C. If you and your roommate both have social preferences such that ui=yi+0.5yj, where yi is player i's payoff, does there exist any pure strategy Nash equilibrium? If does, write down all the pure strategy Nash equilibria. Write the actions and payoffs for this one-shot game in the table below as (your payoff, roommate's payoff), where the winner gets +3, the loser gets 1. If it is a tie, both sides get 2 . D. Does there exist any pure strategy Nash equilibrium if you and your roommate are self-interested? If does, write down all the pure strategy Nash equilibria. E. If you and your roommate both have social preferences such that ui=yi+0.5yj, where yi is player i's payoff, does there exist any pure strategy Nash equilibrium? If does, write down all the pure strategy Nash equilibria