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Question is the row player and player 2 is the column player. Assume preferences are vNM preferences. Two players are playing the following game, where player 1

Question is the row player and player 2 is the column player. Assume preferences are vNM preferences. Two players are playing the following game, where player 1

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Question is the row player and player 2 is the column player. Assume preferences are vNM preferences. Two players are playing the following game, where player 1 L C T 2,0 | 3,2 М 3,4 | 2,0 1.1 Find all the (pure and mixed) Nash Equilibria (NE) of the game. Assume now that players get more actions at their disposal. In particular, the game becomes the following, where n is some real number (not necessarily an integer): L CR T 2,0 3,2 1,3 М 3,4 | 2,0 | 4,2 в 2,0 | п,4 | 2,3 1.2 For what values of n is B a strictly dominated action? Prove and explain your answer. Assuming that B is a strictly dominated action, can you use iterative elimi- nation of dominated actions to solve the game? Explain. 1.3 Assume now that n = 4. Are any actions strictly dominated? Explain your answer. Find all the pure strategy NE. 1.4 Still assuming n = 4, is there an equilibrium in which player 2 randomizes between all three actions? Explain your answer. Find all the mixed strategy NE of the game.
Transcribed Image Text:Question is the row player and player 2 is the column player. Assume preferences are vNM preferences. Two players are playing the following game, where player 1 L C T 2,0 | 3,2 М 3,4 | 2,0 1.1 Find all the (pure and mixed) Nash Equilibria (NE) of the game. Assume now that players get more actions at their disposal. In particular, the game becomes the following, where n is some real number (not necessarily an integer): L CR T 2,0 3,2 1,3 М 3,4 | 2,0 | 4,2 в 2,0 | п,4 | 2,3 1.2 For what values of n is B a strictly dominated action? Prove and explain your answer. Assuming that B is a strictly dominated action, can you use iterative elimi- nation of dominated actions to solve the game? Explain. 1.3 Assume now that n = 4. Are any actions strictly dominated? Explain your answer. Find all the pure strategy NE. 1.4 Still assuming n = 4, is there an equilibrium in which player 2 randomizes between all three actions? Explain your answer. Find all the mixed strategy NE of the game.
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