Bran and Rickon are playing the following game: Each of them chooses an integer from the set {1, 2, ..., 1000} and announces their choices simultaneously. Whoever announces a number that is closest to a half of the average of the two announcing numbers wins 1 dollar, and the other person loses one 1 dollar. (For example, suppose Bran chooses 40 and Rickon chooses 20. Then the average of their two answers is 30, and half of that average is 15. Then Rickon's choice of 20 is closest to this number, and Rickon gets a payoff of 1 dollar, while Bran loses 1 dollar.) If the two announcements are equally close to the half of the average, then the game ends in a draw and nobody wins or loses any money. 1. Does Bran have a strictly dominant strategy? If yes, what is that strictly dominant strategy? If no, explain why. 2. Find all the strictly dominated pure strategies for Bran.