Arizona State University Final Examination December 2023 Game Theory Due: Emailed to me by NOON 12/09/2023 Question 1 2 3 4 5 Total Weight 100 100 100 50 50 400 Score Answer all questions on this test (well, except the last, that ones a bonus). Please include all of your work. An inspirational quote I said to my soul, be still, and wait without hope For hope would be hope for the wrong thing; wait without love, For love would be love of the wrong thing; there is yet faith But the faith and the love and the hope are all in the waiting. Wait without thought, for you are not ready for thought: So the darkness shall be the light, and the stillness the dancing. Page 1 of 7  Game Theory Figure 1: Q1 Game Question 1 Guess Whos Back [25 points each] Refer to Figure 1. 1. Suppose the game in the figure is repeated twice. Both players discount the future by some common 0 = d < 1 2. Construct a (Subgame-perfect) equilibrium in which player 1 gets a payoff of 10 in the first period. 3. How patient must the players be for this to work? 4. What are the equilibrium payoffs? Page 2 of 7  Game Theory Question 2 Pass/Fail? [100 pts] There is a student applying for a job. His type is either A, C, or F (the grade he got in class). If a firm hires a worker of type A, the firms payoff is 1; if a firm hires a worker of type C, the firms payoff is 1/2; and if a firm hires a worker of type F, the firms payoff is 0. Each type is equally likely. The firm will hire a worker if and only if its expected payoff from hiring the worker is (weakly) greater than 2/3. A worker can either disclose her type (grade) or choose pass-fail which yields P if her type is A or C and F if her type is F. A worker gets a payoff of 1 if she is hired and 0 if she is not. [35pts] Does there exist an equilibrium in which every type elects to be graded passfail? Explain. [35pts] Does there exist an equilibrium in which no type elects to be graded pass-fail? [30pts] How do these answers change (or not) if the worker is paid her expected value (rather than the binary hire/not decision)? Page 3 of 7  Game Theory Question 3 Wait! [100 pts] Dwight and Rufus are about to potentially engage in a transaction. Rufus owns some farmland that Dwight is interested in buying. The initial value to the farmland is 0 (to both parties) and if Rufus makes some improvements, the value is 1 to him and 3 to Dwight. It costs 2 to Rufus to make the improvements. The timing of the game is as follows. First, Rufus decides whether to make the improvements. Second, Dwight observes some information about this (well specify this shortly). Third, Dwight makes a take-it-or-leave it offer to Rufus. You may assume that Rufus accepts any offer that yields him a value weakly higher (=) than his current value for the land. i. (35 pts) Suppose Dwight observes Rufus investment decision perfectly. Is there an equilibrium in which Rufus invests? Is there one in which Rufus does not invest? ii. (35 pts) Suppose Dwight does not observe Rufus investment decision. Is there an equilibrium in which Rufus invests? Is there one in which Rufus does not invest? iii. (30 pts) Compare the answers for ii. and iii. to that for i. If there are issues, can you think of any remedies (contractual, informational, timing...)? Page 4 of 7  Game Theory Question 4 Your Favorite Topic[50 pts] Pick your favorite topic from this class...Why was it your favorite? Explain what we learned. Explain the mechanics behind what we found. Any applications/illustrations of this that you find compelling? Page 5 of 7  Game Theory Question 5 Your Least Favorite Topic[50 pts] Pick your least favorite topic from this class...Why was it your least favorite? Explain what we learned. Explain the mechanics behind what we found. Page 6 of 7  Game Theory  End of Examination  Page 7 of 7  Game Theory

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