In the bounty regulations, I am missing regulations which say when a bounty can be awarded at the earliest. It seems natural to me (and in the interest of the person placing the bounty, who wants the best possible answer) that no bounties should be awarded before the bounty period (7 days) is over. Like in any other public call for bids, deadlines are set and you cannot award prematurely.
It is also fair to people who are working on solutions to give them the full bounty period to present their solutions. Clearly, credit is given to the first, i.e. if a person has already presented an answer and a later person had the same or similar ideas, then he/she cannot copy them and have to quote earlier answers if relying on these ideas. The usual academic procedure.
However, bounties happen to be awarded prematurely which is certainly demotivating for people still working on the problem.
Reasoning as laid out above, I suggest to include as an additional rule that no bounties shall be awarded before the bounty period is over.