the following question is a kind of Rubinstein bargaining model:
2 players, A and B, have 100dollars to divide between them. They agree to spend T days negotiating over this division.
The first day, A will make an offer, B either accepts or comes back with a counteroffer the next day, and on T day, B gets to make one final offer. If they cannot reach an agreement in T days, both players get 0 dollar.
Assuming that both A and B are having the same degree of impatience: A and B discount payoff in the future at a rate of r per day.
Finally, we assume that if a player is indifferent between two offers, he wil accept the one that is most preferred by his opponent.
This idea is that the opponent could offer some arbitrary small amount that would make the player strictly prefer one choice and that this assumption allows us to approximate such an"arbitrarily small amount" by zero. It turns out that there is a unique subgame perfect nash equilibrium of this bargaining game.
So the question is that, what is the SPNE in this alternating-offer bargaining game when T is even?
Am i making it much clearer?
Thanks for all the advice that has given on modifying this question, thanks for being patient for my stupid question.