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GTMIdterm1S2021UnderGrad Game Theory: ECON 3160 Midterm 1 Spring 2021 Name: Answer Sheet 1a 1b 1c 2a 2b 3a 3b 4 5a 5b 6 7a 7b 8a T or F 8b T or F 8c T or F 8d T or F 8e T or F Name: Point allocaIons are given aKer each quesIon. 1. Consider a situaIon between a firm and a job applicant. IniIally the firm must decide whether to offer a job to the applicant. Following this decision, the firm must decide whether to offer the applicant a high salary or a low salary. The applicant can then decide whether to accept the offer or to reject it. a) Draw this game in extensive form (without payoffs). (3) b) Draw this game in normal (strategic) form (without payoffs). (3) c) State the strategy space for the firm. (Remember that a strategy is a fully conIngent plan.) (3) 2. In the following game player 1 has three strategies {A,B,C} and player 2 has three strategies {D,E,F}. a) Calculate the expected payoff of strategy A if player 1 believes that player 2 will play a mixed strategy of ½ D and ½ F. (3) b) Are any strategies in this game strictly dominated by a pure strategy? If yes, state which strategies are dominated and the strategy that dominates it. (3) D E F A 2,2 3,1 0,3 B 3,2 4,3 1,1 C 1,2 1,0 2,3 3. In the following game player 1 has three strategies {A,B,C} and player 2 has two strategies {D,E}. a) Are any strategies strictly dominated for player 1? If so list them and the strategy that dominates it. You should consider pure and mixed strategies in this game. (Be specific.) (3) b) Are any strategies strictly dominated for player 2? If so list them and the strategy that dominates it. You should consider pure and mixed strategies in this game. (Be specific.) (3) 4. In the following game player 1 has three strategies {A,B,C} and player 2 has two strategies {D,E}. Are any strategies strictly dominated for player 1? If so list them and the strategy that dominates it. You should consider pure and mixed strategies in this game. (Be specific.) (3) D E A 1,2 4,1 B 3,1 3,3 C 4,0 1,1 D E A 0,3 3,1 B 3,1 0,3 C 1,2 1,2 5. In the following game player 1 has two strategies {A,B} and player 2 has two strategies {C,D}. a) Find all Nash Equilibrium(s) for this game. (3) b) List all (Pareto) efficient strategy combinaIons for this game. (3) 6. In the following game player 1 has three strategies {A,B,C} and player 2 has three strategies {D,E,F}. Find the set of raIonalizable strategies for this game. (5) C D A 9,3 6,6 B 8,0 7,1 D E F A 0,5 2,3 2,3 B 2,3 0,5 3,2 C 5,4 3,2 2,3 7. In the following game player 1 has three strategies {A,B,C} and player 2 has three strategies {D,E,F}. a) What are the raIonalizable strategies of this game? (2) b) What is(are) the Nash Equilibrium(s) of this game? (3) 8. Answer true or false for each quesIon statement below: (2 points for each) a) A raIonalizeable strategy is always a Nash Equilibrium. True False b) Iterated removal of weakly dominated strategies is order independent. True False c) Iterated removal of strictly dominated strategies is order independent. True False d) A Nash equilibrium strategy combinaIon is always (Pareto) efficient. True False e) A Nash equilibrium strategy combinaIon is always Pareto dominant. True False D E F A 2,5 3,3 2,3 B 3,3 2,5 3,2 C 5,0 3,3 1,3