Guessing the Average) A group of 1000 people are asked to privately submit a number between 0 and 100. The winners are those whose submissions are closest to 2 / 3 of the average submission (the average being equal to the sum of all submissions divided by 1000). All winners earn 100 dollars, all other players earn nothing. Solve for a Nash Equilibrium of this game. (Hint: consider the same game but for a group of 2 players. How should they \"best respond\" to each other?)