No.. People would just hit someone a lot, put a huge bounty, and then kill them with a single arrow.
And besides that, it gives no sense for tributes to be able to put bounties on someone. From Wikipedia:
A bounty
(from Latin bonitās, goodness) is a payment or reward often offered by a group as an incentive for the accomplishment of a task by someone usually not associated with the group.
Like KRadium said, you wouldn't gain any points because you'd just be recovering the points you lost.
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Back to topic. I'm taking a slightly controversial viewpoint on this. I feel as though this is a brilliant idea! Players would be able to speed up the game because there would be more incentive to fight. Here are some examples of how it could be used:
1) There are 5 players left and a team of 2 is wrecking havoc. You bounty one of the players, and immediately the other 2 players come out to help fight, rather than you fighting them yourself and almost definitely dying. This is a strategy to help you stand a chance.
2) You are in Pre-Deathmatch, and both of the others are pointing bows at you. However, they aren't teamed. You quickly bounty one of them, and immediately one of the bows is pointed in a different direction.
These are just some of the situations in which this idea would be helpful and practical. If there's no real harm in it and there is interest for it, then add it!
Btw, what is the problem in bountying points to a friend? Is there a harm in having your friend kill you if you want to transfer points?