HMMT 2011 S1

Tom, Dick, and Harry play a game in which they each pick an integer between 1 and 2011. Tom picks a number first and informs Dick and Harry of his choice. Then Dick picks a different number and informs Harry of his choice. Finally, Harry picks a number different from both Tom's and Dick's. After all the picks are complete, an integer is randomly selected between 1 and 2011. The player whose number is closest wins 2 dollars, unless there is a tie, in which case each of the tied players wins 1 dollar. If Tom knows that Dick and Harry will each play optimally and select randomly among equally optimal choices, there are two numbers Tom can pick to maximize his expected profit; what are they?