A grandfather writes his will and has to decide how much money he will leave to his three children: Sean, Tom and Brad. The grandfather has the following plan. Each of his children should write independently and at the same time a sum of money between 10 and 1,000,000 GBP on a piece of paper. The child who writes the lowest amount of money will receive that amount and the other will have no choice. For example, if Tom writes 500,000 pounds and the other two children 750,000 pounds, then Tom gets the 500,000 pounds and Sean and Brad get nothing. If one of the children writes the same amount (and this usual amount is the lowest), this amount is split equally.
What is the Nash balance of this game?