Question: Two players pick a number in [0,1]. The player whose number is closest to half the average of the two numbers gets +1, the other

Two players pick a number in [0,1]. The player whose number is closest to half the average of the two numbers gets +1, the other player gets -1. If both players are equally close, they get zero.

Suppose player 1 picks x (0 < x 1). What is the set of best responses for player 2? And, what is the Nash equilibrium for this game?

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