Speaking from the hockey stand point, at one time players were required by the NHLPA to sign autographs, and the money went directly into the players retirement fund, and pooled accordingly to those that were drawing from the fund. Thoughts were that at some point these players would benifit from that down the road a ways. Older products like Be A Player were strictly handled this way, and in fact some of the players who do not like to, or want to sign autographs for card companies could only be found in this product, because basically the players association made them do it. It may be different now, I am not entirely sure, as I am talking about the late 90s, and early 2000s.
As far as paid sit down public events, it is up to the promoters, and the player agents to work out a price per autograph, or a specific lump sum amount for a specific time period. Determining prices basically comes by the popularity of the player involved, and these agents, or agencies that promote their player know exactly what they can get for each individual player. I can tell you my friend who owns Frozen Pond in Toronto was charged $15,000 for 2 hours of Alexander Ovechkins time. This is the kind of money you have to pay to get them in for an appearance. People wonder why these stores charge $100 for an auto, well there is why right there.