Consider the following situation: 3 participants are asked to simultaneously submit an integer number between 0 and 5. The winner of the contest is the person(s) whose number is closest to -times the average of all numbers submitted. The winner gets a prize of 100, the others participants get 0. If there are more winners, the prize is split between them.

a.) Assuming p = 1 find all Nash equilibria in pure strategies

b.) Find all Nash equilibria when p>1