5. Two players i = 1,2 can choose any number x; between 0 and 1. The...

 

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5. Two players i = 1,2 can choose any number x; between 0 and 1. The player who chooses the smaller of the two numbers wins a prize equal to the number that he chose. If both players chose the same number, they both get one half of the number they chose. Thus, if i is either 1 or 2, and j is the other player, then utilities can be written as follows: xi if xi < xj ui (x1, x2) = if x = xj 0 if xi > xj Find the pure strategy Nash equilibria of this game. 5. Two players i = 1,2 can choose any number x; between 0 and 1. The player who chooses the smaller of the two numbers wins a prize equal to the number that he chose. If both players chose the same number, they both get one half of the number they chose. Thus, if i is either 1 or 2, and j is the other player, then utilities can be written as follows: xi if xi < xj ui (x1, x2) = if x = xj 0 if xi > xj Find the pure strategy Nash equilibria of this game.