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You and one of your classmates are selected to play a game. In this game, both players would write down a number between 0 and 10 simultaneously. If the sum of the two numbers is 10, each of you can get the same amount of dollars as the number each of you wrote. Otherwise, both of you get nothing. Answer the following questions with game theory knowledge.
(a) Do we have any pure strategy Nash equilibrium in this game? Explain your answer
(b) Which number would you choose and why you choose that number?
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