Quiz 25. Game Theory Ans

# Quiz 25. Game Theory Ans - (a) . What is a subgame perfect...

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Shomu Banerjee ECON 201 GAME THEORY ANSWERS (a) Fill in the payoffs for each player in the matrix below: Stay out Enter Ann's actions Tom's actions Use labor Use robot 900, 0 400, 300 500, 0 132, -36 (b) Does either Tom or Ann have a dominant strategy? If so, what is/are it/they? Tom’s dominant strategy is ‘Use labor’ (900>500 and 400>132); Ann does not have one. (c) What is a Nash equilibrium in this game if both players choose their actions at the same time? (Use labor, Enter) (d) Consider the sequential game where Tom is the leader and chooses his action first followed by Ann as shown by the tree below: Tom Ann Ann Use labor Use robot Stay out Enter Stay out Enter (132, -36) (500, 0) (400, 300) (900, 0) The payoffs are the same as what you calculated in
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Unformatted text preview: (a) . What is a subgame perfect equilibrium in this game? Use backward induction. Consider the subgame when it is Ann’s turn to move at the node on the left; Ann chooses ‘Enter’. Then consider the subgame when it is Ann’s turn to move at the node on the right; Ann chooses ‘Stay out’. The next subgame is the whole game itself at the initial node. Tom can choose ‘Use labor’ and end up with 400 or choose ‘Use robot’ and make 500, which is better. Therefore the Nash equilibrium in the leader follower game is (Use robot, Stay out). This example shows the value of commitment: an action that is dominated in a static game may be the optimal choice in a dynamic game....
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## This note was uploaded on 10/26/2010 for the course ECONOMICS ECON 201 taught by Professor Dr.shomubanerjee during the Summer '07 term at Emory.

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