A grandfather is writing his will and must decide how much money he will leave to his three children: Sean, Tom, and Brad. The grandfather comes up with the following plan. Each of his children is to independently and simultaneously write an amount of money on a piece of paper between £10 and £1,000,000. The child who writes the lowest amount of money will receive that amount, and the others will be left with nothing. For example, if Tom writes £500,000, and the other two children write £750,000, then Tom will get the £500,000 and Sean and Brad will get nothing. If any of the children write the same amount (and that common amount is the lowest), they will split that amount equally.
What is the Nash equilibrium of this game?