# A1 - CSC 5350 Assignment 1 Due date: 12 October 2009 1....

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CSC 5350 Assignment 1 Due date: 12 October 2009 1. Consider a 3-player strategic game ,( ),( ) ii G N A u . Each player has three available actions: 1 a , 2 a and 3 a . That is,  1 2 3 1 2 3 { , , } A A A a a a . Suppose in G , player 1 always receives a payoff of 10 if he plays 1 a , or 0 otherwise, regardless of what strategies the other two players play; player 2 always receives a payoff of 5 if he plays 2 a , or 0 otherwise, regardless of what strategies the other two players play; player 3 always receives a payoff of 2 if he plays 3 a , or 0 otherwise, regardless of what strategies the other two players play. (a) Give the payoff matrix of G . (b) What are the pure strategy Nash equilibria in G ? (c) An outcome of a strategic game is said to be Pareto optimal if there is no other outcome existing in the same game, such that at least one player i gets a higher payoff in than in , while no player gets a lower payoff in than in .

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## This note was uploaded on 04/23/2010 for the course CSC CSC5350 taught by Professor Leunghofung during the Winter '09 term at CUHK.

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A1 - CSC 5350 Assignment 1 Due date: 12 October 2009 1....

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