There is an elemination game with 10 unkown players. There are 8 rounds. At the end of each of the first 7 rounds, 1 player is eliminated. In the last round, the winner will be decided between the remaining 3 players.
After every round (of the first 7 rounds) gamblers can bet on the eventual winner. Also, after every round, more is known about the players, so it's more impressive if you know at the beginning of the tournament already who is going to win. How should we arrange the pay-outs for the bets? Should we force people to pick exactly on potential winner every round or allow for indecision/more involved strategies?
(I know this is maybe a bit involved but if someone knows pointers to the right theory, I think I might be able to work it out on my own. I just don't know what to search for and I don't find the right theory with the most obvious searches.)