It is a game theory question

Question 2. [25 total points] \"Holding to account.\" Professor Xi has hired Wayne as a summer research assistant to work in her lab. Wayne can either work hard or shirk. Working hard costs Wayne 8 but generates research worth 90 for Professor Xi. If Wayne shirks, it costs him nothing and it produces nothing for the Professor. Professor Xi cannot observe directly whether Wayne works hard or shirks but she can decide whether or not to review Wayne's work. If Professor Xi does not review Wayne's work, she will not know whether or not he has worked hard. In this case, Professor Xi must pay Wayne a wage of 12 and write him a letter of reference which is also worth 12 to him and costs her 12 to write. If Professor Xi reviews Wayne's work, she will discover whether or not Wayne has worked hard. If Wayne has worked hard, again Professor Xi must pay Wayne 12 and write that letter of reference. But if Professor Xi reviews Wayne's work and nds that he has shirked then Professor Xi only pays Wayne his wage of 12 and she does not write him a letter of reference. The cost to Professor Xi of reviewing Wayne's work is 8. Take Professor Xi's payoff to be the value of the research (if it exists) minus any wages paid to Wayne minus the cost of reviewing Wayne's work [if she reviews) minus the cost of writing a reference letter (if she does write one for him). Take Wayne's payoff to be his wages plus the value of the letter of reference (if Professor Xi writes him one) minus his cost of working (if he works). Page 2 of 5 Strategic Thinking. an introduction to game theory (ECON2141) (a) [10 points] Suppose that Wayne can observe whether or not Professor Xi chooses to review his work before he chooses whether to work or to shirk. Write down the game tree and explain whether or not Professor Xi will chosse to review his work. What will be their payoffs? (b) [15 points] Now suppose that Wayne cannot observe whether or not Professor Xi will review his work. Write down this game tree. Solve for the equilibrium [strategies and payoffs) in this game