Q1. Consider the following game played by three people. Each person simultaneously writes down a number...

 

 

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Q1. Consider the following game played by three people. Each person simultaneously writes down a number from {1, 2, ..., 10), i.e. an integer between 1- 10. 1 Let the number chosen by player i be denoted by X. Whichever player has the number closest to the average, (X + X2 +X3), pays an amount equal to the number he or she wrote down. The other two players pay 5. For example, if x=2, X2=4 and x3=7, then the average is (2+4+7)=;so, player 2 pays 4, as his number is closest to the average, and players 1 and 3 each pay 5. The payoff to each player is the negative of the number he or she pays. In other words, if a player pays 5, her payoff is -5. Can you find a Nash equilibrium in this game where everyone chooses the same number? Q1. Consider the following game played by three people. Each person simultaneously writes down a number from {1, 2, ..., 10), i.e. an integer between 1- 10. 1 Let the number chosen by player i be denoted by X. Whichever player has the number closest to the average, (X + X2 +X3), pays an amount equal to the number he or she wrote down. The other two players pay 5. For example, if x=2, X2=4 and x3=7, then the average is (2+4+7)=;so, player 2 pays 4, as his number is closest to the average, and players 1 and 3 each pay 5. The payoff to each player is the negative of the number he or she pays. In other words, if a player pays 5, her payoff is -5. Can you find a Nash equilibrium in this game where everyone chooses the same number?