Midterm and Solution

# Midterm and Solution - University of British Columbia...

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University of British Columbia Department of Economics Economics 221 (002) Introduction to Strategic Thinking Winter Session Term I, 2008/09 Midterm Examination - Solutions PART A: 1. Find the Subgame Perfect Nash Equilibrium to the following game: U M D 1 2 H (5,1) (2,9) (10,2) (4,8) L (3,2) (6,4) Astrategyforp layer 1 will specify a single action. A strategy for player 2 will specify an action to take at the upper information set andanac t iontotak ea tthelow e r decision node. Applying backwards induction, at the lower decision node for player 2 ,p laye r 2 will want to play L ( 8 > 2 ). In the upper portion of the game, this is a simultaneous move game Player 2 HL Player 1 U (3 , 2) · (6 , 4) · M · (5 , 1) (2 , 9) · and player 2 will play L in the upper information set. Player 1 will choose between U (giving a f nal outcome at U,L 6 for player 1) and D (giving a f nal outcome D,L 4 for player 1) . 1 chooses U. The subgame perfect Nash equilibrium is: { player 1 strategy, (player 2 action at upper info. set, player 2 action at lower info. set) } = { U, ( L,L ) } Note that ( L,L,L ) does not describe an appropriate strategy for player 2 since they can’t di f erentiate between 1 playing U or M . 1

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2. Convert the following game tree to a game matrix and f nd the Pure Strategy Nash Equilibria of the game: 1 2 U D L R (2,5) (6,8) (5,2) (7,4) Player 2 L,L L,R Player 1 U (2 , 5) (2 , 5) D · (5 , 2) · (7 , 4) · R,L R,R · (6 , 8) · (6 , 8) · (5 , 2) · (7 , 4) · There are 3 Pure Strategy Nash Equilibria: { U, ( R,L ) } , { D, ( L,R ) } , { D, ( R,R ) } 2
3. What is a dominant strategy? In a 2 player, 2 action (each player has two available actions) game, if player 1 hasadom inantstrategy ,isitposs ib leforthegametohave a mixed strategy Nash Equilibrium?

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## This note was uploaded on 12/01/2011 for the course ECON 221 taught by Professor V during the Winter '09 term at BC.

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Midterm and Solution - University of British Columbia...

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