Answer Happy

2. Ann, Brian and Carla decide to bring some excitement into their lives with the help of their uncle Sam. Each of them is going to secretly write a number chosen from the set 2,3,4 on a piece of paper and hand it to Sam. Sam computes half the average of the three numbers, call it a, and determines the winners as those whose number is closest to a. For example, suppose that Ann writes 2, Brian writes 2 and Carla writes 4. Then a = (²+2+¹) = 1.33 and the winners are Ann and Brian. Sam then hands out money as follows: nothing to the loser(s), $2 to the winner if there are no ties and $1 to each of the winners if there are tics. Thus in the above example, Ann and Brian get $1 cach and Carla gets nothing.
Revisit Question 2 of Problem Set 1 and find all the Nash equilibria of that game. Is there a difference between the Nash equilibria and the dominant strategy equilibrium you found in Problem Set 1, Question 2(d)?