Compute the Nash equilibria of the following location game. There are two
people who simultaneously select numbers between zero and one. Suppose
player 1 chooses s1 and player 2 chooses s2 . If si = sj , then player i gets a
payoff of (si + sj )/2 and player j obtains 1 − (si + sj )/2, for i = 1, 2. If
s1 = s2 , then both players get a payoff of 1/2.
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