Instructions: This is a take home exam. You are supposed to work INDIVIDUALLY. Questions are written in a way that there cannot he answers alike, except for some calculation problems. If I suspect two exams are highly similar, the two exams will be graded a w. Do not jeopardize your grade nor your graduate standing by working or using other student work. The due date is Friday December 30 by 13:10. To submit your take home exam response, you will log into university's TronClass and upload the exam answer le. Only one exam answer le can be uploaded. Students will not be permitted to submit any additional work or an alternative version. Only the original submission will be forwarded for grading. You must show all work for these problems. 2. Consider the following game that you must be familiar with: Rock, Paper, Scissors. If both players form the same object then they tie and receive 0. If one player forms a Rock and the other forms Scissors then Rock wins and receives a payoff of 1 While Scissors loses and receives a payoff of -1. If one player forms Scissors and the other forms Paper then Scissors wins and receives a payoff of 1 while Paper loses and receives a payoff ofl. If one player forms Paper and the other forms Rock then Paper wins and receives a payoff of 1 and Rock loses and receives a payoff of -1. (20 points.) a. Please create a 3x3 payoff matrix of this Rock, Paper, Scissors game. b. Is there a dominant strategy, strategy that is optimal no matter what an opponent does, for each player? 0. Are the results from part b consistent with your strategies when you are playing the Rock, Paper, Scissors game? d. What is the Nash equilibrium in the Rock, Paper, Scissors game