Blood Sport: This, obviously, gets much easier when you have noetic backup technology to ensure that you don’t run out of people quite as fast as you otherwise might. Even so, in the Empire and other civilized polities, this is usually limited to martial arts competitions where death is mostly accidental, and minor outgrowths of duelling culture.
Elsewhere, some downright horrifying examples also exist thanks to the export versions of the tech… but what can you do? Barbarians gonna barbar.
Duel To The Death: Available, but strongly discouraged (after all, Immortal Life Is Really Damned Expensive), unlike duels to the non-death – or, in the modern era, to rephrase that, duels to the permadeath are this, and duels to the death are, well, more permitted since death is not permanent, as a rule.
Nonetheless, permitted under certain constrained circumstances, including the same not while you retain any open commitments clause that covers voluntary suicide, because sometimes when two people really genuinely cannot tolerate each other’s existence – well, what else can you do? Do you want a moment of agony, or an entire history of ache?