Comment by ball_of_lint

Each player can limit the other's income to $0 - the offerer can offer $0 and the receiver can reject any deal.

So then what's optimal? $50 seems obviously fair, but does that mean we ought to reject offers of $49 100% of the time? Not quite, to limit the opponent's expected income for an offer of $49 to $50 instead of the $51 they left for themselves, we can use a mixed strategy that only accepts the offer with probability 50/51. Extending that gives the opponent a benefit curve that is linear as they leave themselves more money up to $50 and then flat at $50 afterwards.

That's good, but we can make it better - if we accept offers for $X<$50 with probability 50/(100-X) - epsilon*(50-X), then their expected benefit curve is smooth and has a peak at $50, which is the most we can expect to make except against a generous opponent.

After all that, playing this game as stated against an unknown opponent there's a lot of uncertainty. Maybe all your opponents are entirely irrational and move at random. Maybe all your opponents have colluded and decided that $66 for the offerer and $34 for the receiver is fair and that's the only deal they'll make. But if you think that random actors in the universe are reasonably intelligent and can discover the equilibrium above with the thought worth putting into this Ultimatum game, the receiver strategy above properly aligns incentives.