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# Behavioral Economics question?

Consider a guessing game with N people, and the person closest to 20 plus 1/2 of the average is awarded the prize, which is split in the event of a tie. The range of guesses is from 0 to 100. Show that 40 is a Nash equilibrium. (Hint: Suppose that N-1 people choose 40 and one person deviates to x < 40. Calculate the target as a function of the deviants decision, x. The deviant will lose if the target is greater than the midpoint between x and 40, i.e. if the target is greater than (40 + x)/2. Check to see if this is the case.)

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