Yes there are actually some pretty big adjustments, that need to be made in tournaments with bounties. Not so much, when stacks are deep, and the pot is small. But when somebody is all-in, and you cover them, you need to call wider, because their bounty is giving you better pot
odds. And because other players might want the bounty to, you sometimes need to be very aggressive in isolating an all-in player, particularly if they are very short.
Also there is much less value in outlasting other players, because only half the price money is distributed based on finishing position. So where ICM cause us to be quite risk averse in normal tournaments, bountys kind of negate that and reward a much more aggressive approach, where the goal is to build and maintain a big stack even at the expense of cashing less frequently.
Lets say for example, that you are playing a 9-man SnG. In the first hand you open raise to 3BB with AKs, it folds to SB, who ships his 75BB into the pot. It folds to you, and based on a population read you expect, that most of his range is small to medium pocket pairs and sometimes another AK. In that case the play in a normal 9-man SnG is to fold, because dubbling your stack dont dubble your EV. But in a bounty 9-man you should call, because now you more than dubble your EV, if you win, since 25% of the buyin is already in your account in the form of his bounty.
Another adjustment is, that if you want to bet the river for value and have to choose between making a small bet or putting your opponent all-in, then you should lean far more towards the latter option, so you give yourself a chance to win his bounty. And as others have already said, if you become short, so that the chip value of your bounty is very significant compared to your stack, you wont have fold equity, and this will change your jamming range. The value of hands like 44 or JTs goes down, whereas the value of hands like KJo or A9o goes up, because they dominate part of your opponents calling ranges.
