Take Home Midterm ExamFIN 750Winter 2001Galina SchwartzUniversity of MichiganBusiness SchoolTake Home Midterm ExamFIN 750Winter 2001Galina SchwartzUniversity of MichiganBusiness SchoolMaximum score for each question is in brackets. Please, make youranswers as short as you can1. [20] Choose any two of the following statements. For each one you choose, saywhether it is true or false. If true, give a brief argument explaining why it is true. If false,give a brief example where the statement can be seen to be false.(a) [10] In a sequential move game, the first mover can always win.(b) [10] If one player in a simultaneous-move game has a dominant strategy, then theoutcome of the game will not change if this player is allowed to make the first move.(c) [10] A repeated prisoners’ dilemma will lead to a cooperative outcome so long as it isrepeated more than 10 times.2. [30] In a scene from Manhattan Murder Mystery, Woody Allen and Diane Keaton areat a hockey game in Madison Square Garden. She is obviously not enjoying herself, buthe tells her: “Remember our deal. You stay here with me for the entire hockey game, andnext week I’ll come to the opera with you and stay until the end.” Later, we see themcoming out of the Metropolitan Opera House into a deserted Lincoln Center square whileinside the music is still playing. Keaton is visibly upset: “What about our deal? I stayedto the end of the hockey game, and you were supposed to stay till the end of the opera.”Allen answers: “You know I can’t listen to too much Wagner. At the end of the first act, Ialready felt the urge to invade Poland.” Comment on this scene from a strategicperspective.3. [50] Suppose that a person owes $100 in taxes to the government. The person caneither pay the $100 or cheat and pay nothing. The government can either audit this personor not audit him; the decision about whether to audit is made without knowing whatchoice the person made. If the government audits a person who picked Cheat, the taxevasion is discovered and the person must pay $150 to cover both his taxes and a fineimposed on detected cheaters. Auditing is costly; when the government audits a person,both the government and the person lose $10 (this cost must be paid regardless ofwhether the person chose Cheat or Pay). The payoffs in this non-constant-sum game aremeasured so that (for example) if the person choosesGame Theory applications to Finance and Consulting CasesPay and the government chooses Not audit, the person’s payoff equals 0 and thegovernment’s payoff equals 100.(a) [10] Fill in the two missing numbers in the following payoff matrix.GovernmentAudit NotPerson Cheat (-60, 140) ( , 0)Pay (-10, ) (0,100)(b) [10] Determine whether there is an equilibrium in pure strategies in this game.(c) [10] Suppose that the government chooses Audit with probability q (and, obviously,chooses Not with probability 1 – q). Determine the value at which q must be set to ensurethat the person gets the same expected payoff from Cheat as he gets from Pay (this isequivalent to asking you to find the value of q that holds in a mixed-strategy equilibriumin this non-constant-sum game).(d) [10] Suppose that the person feels (somewhat) guilty when he chooses Cheat. We willrepresent this feeling of guilt by saying that the person’s payoff when he chooses Cheat(whether he is audited or not) falls by 20. In this case, at which value must q be set toensure that the person gets the same expected payoff from Cheat as he gets from Pay?(e) [10] Compare the outcomes from parts c and d. Bearing in mind the probability withwhich the government chooses Audit, would you expect to see any difference betweenthe person’s equilibrium behavior in part c and his equilibrium behavior in part d? If not,is there any benefit to society from the person’s guilty conscience in part d?Game Theory applications to Finance and Consulting