ECON2112 Midterm S1 2011 -...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Name:_____________________________ SID:_______________________ Tutor’s Name:_______________________ Tutorial Day & Time:_________________ SCHOOL OF ECONOMICS ECONOMICS 2112 GAME THEORY AND BUSINESS STRATEGY S1 2011 MIDTERM EXAM This exam comprises of 12 pages including this cover page. There are 10 questions. Answer all 10. Questions answered correctly are worth 3 marks. Questions answered incorrectly are worth -1 mark. Questions not answered are worth 0 mark. Total time allowed: 60 minutes Report your Student ID number (SID) at the top of each page. Any evidence of dishonesty will be punished by failure and reported to the appropriate authority 1 SID:_________________________ 1. Consider the following three-player game: L C R 1,2,2 0,3,2 1,2,9 2,1,7 ,1,0 2,2,1 T B X For which values of a) b) c) d) and and is the strategy T B L C R 0,3,0 ,3,1 1,2,2 2,1,2 3,1,4 2,2,3 Y weakly dominated but not strictly dominated? . . . . 2. A normal form game is defined by: a) A payoff matrix. b) A set of players, a strategy profile for each player, and a Bernoullian utility function for each player defined over the set of strategy profiles. c) A set of players, a strategy profile for each player, a Bernoullian utility function for each player defined over the set of strategy profiles and a Nash equilibrium. d) Two players and a matrix. 3. Let and suppose that an agent’s preferences are characterized by a Bernoullian utility function that satisfies . Select the correct statement. a) The agent strictly prefers the lottery to the certain outcome . b) The Bernoullian utility function defined by , represents the same preferences over lotteries as . c) The agent strictly prefers the lottery to the certain outcome . d) The agent is risk averse. and 2 SID:_________________________ 4. Consider the game: L 3,3 2,2 1,0 T M B C 2,2 2,2 1,1 R 0,1 1,1 1,1 Select the correct statement: a) , , are the Nash equilibria in pure strategies of the game. The unique equilibrium in mixed strategies is . b) is an equilibrium in dominant strategies. c) , , , , and are all the Nash equilibria o f the game. d) This game has three Nash equilibria, of which only two are admissible (i.e., undominated). 5. Given the following game: L 6,2 1,1 L 7,2 4,0 T B R 1,1 2,6 R 4,0 5,6 What is the set of Nash equilibria? a) b) c) d) . . . . 6. Given the following game: T B What is the set of Nash equilibria? a) b) c) d) . . . . 3 SID:_________________________ 7. Given the following game: L 5,5 9,2 T B R 7,3 2,8 Select the wrong statement: a) T and R are the players’ pure Minmax strategies. b) is the Row player’s Nash equilibrium strategy and is the Column player’ Nash equilibrium strategy. c) For this type of game, the players’ mixed Minmax strategies are the same as their Nash equilibrium mixed strategies. d) is the Row player’s mixed Minmax strategy and is the Column player’ mixed Minmax strategy. 8. Given the following game: T B L 7,2 4,0 R 4,0 5,6 RR 7,1 3,2 Select the correct statement: a) The strategy RR is weakly dominated but not strictly dominated. b) The set of Nash equilibria is . c) The set of Nash equilibria is the same in Question 6. d) is the welfare-maximising Nash equilibrium because it maximizes the sum of the payoffs. 9. Select the correct statement: a) b) c) d) If is a dominated strategy then either A or B is also a dominated strategy. An admissible (i.e., undominated) equilibrium must be a strict equilibrium. If is a dominated strategy then is also a dominated strategy. In every game, each player has a mixed strategy that is a dominant strategy. 10. Consider a normal form game strategy profile a) b) c) d) For each For each For each For each , . Select the wrong alternative. A is a Nash equilibrium if: is a best response against and every , and every , and every , . . . . 4 ...
View Full Document

This note was uploaded on 06/19/2011 for the course ECON 2112 taught by Professor Arghyaghosh during the One '10 term at University of New South Wales.

Ask a homework question - tutors are online