Perhaps this has already been covered and I missed it (though I did look):
Player A has the right to offer a proposal, but player B has the right to reject it.
The controls are different, but are pretty much balanced.
"Logic" means "devoid of emotion."
Rationality takes into account human nature and realistic (though perhaps emotional) consequences.
The only significant advantage I can think of is that Player A gets to make the proposals at a time and place of his choosing, initiating any possibilities. Player B doesn't get that control.
What could change the situation is if they have to be sitting together at an agreed upon time and duration for any proposal to be made as well as to be rejected or affirmed. Or, if they had a time limit.
If Person B were allowed to wait on announcing his decision, that too would nullify any advantage Player A has.
If I'm not making my point, try this example (or ignore it if you get my meaning):
Player A could sit there for five minutes silently, knowing what his next proposal would be and when he would offer it. Psychologically, this gives Player A the edge as he is the instigator and Player B can only respond when Player A relinquishes control.
This would be an edge simply because it might cause player B more stress or test his patience more.
On the other hand, Player B could wait for A to make a proposal and then do the same thing back; refuse to answer until a time and place of his choosing, knowing what his answer will be and when it will come, and that Player A can't make another proposal until this one is accepted or declined.
If there's a time limit on the negotiations, then that completely negates any power either of them have to control each other, emotionally or otherwise.
Likewise if the negotiations can be ongoing over a long period, but both must schedule and agree to the times for negotiations, there is no advantage for either side.
The only edge Player A gets is one of perception, and only at first. Shortly after that the same advantage is given to Player B - although if Player B doesn't realize he has that advantage it can be lost - but then again the same is true of Player A.
The actual good sense economic model here is to maximize efficiency, make the most profit possible, and to do a cost/benefit analysis.
The real and accurate answer would be to maximize profit as quickly as possible and get on to other things. If this deal can be made in 10 seconds, then it's very profitable indeed. If it takes an hour, the profitability is greatly reduced for all parties. If it takes more than an hour, it probably actually cost the Players something to be there and they both lose.
The best answer from an intelligent economist would be to offer the 50-50 split right out the gate, to maximize profit in the shortest period of time, reducing the cost of a cost/benefit calculation - thus amplifying the benefit.
A fast, neat, efficient, 50-50 deal is actually what is in the best interest of both parties, and not by "just a little bit."