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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.

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    I think you need to be more specific about the rules of the game $p_1$ and $p_2$ are playing.2012-11-23
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    beauby i have modified it a bit, hope this could explain more about this question, thanks!2012-11-23
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    You should tell us what an offer is and what it means to accept an offer.2012-11-23
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    what i only know is that there is an amount of money to be shared by 2 players,2012-11-23
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    and player 1 would take the first turn to give an offer to player 2(in T=1), what player 2 can do is to accept the offer and the game ends, if this is not the case, player 2 will give an offer to player 1 in the next period (T=2) then this time for player 1 to decide whether to accept it or give player 2 a new offer(in T=3). and the important thing is that, the money being shared today will cost more than that when they end the game in later period and the discounting factor is r.2012-11-23
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    is it possible to have solution base on this amount of information?2012-11-23
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    the offer maybe of player 1 says he will give $0(total of 10$) to player 2, thus if player 2 accept, he will get $10 and she will get $0, but player 2 could choose to make a new offer to player 1 base on the discounted amount of money 10xr... and so on, this is just an example, i think the amount offered should be base on backward induction2012-11-23
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    About half of the basics of the question are hidden in the comments; the question is unintelligible in its present form, not least because the parameter $r$ isn't introduced. Please edit the question to reflect all the essential information that you've added in the comments; people shouldn't have to dig through the comments to piece together the question.2012-11-23
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    Also, please don't use exclamation marks in the title; the title is just as noteworthy as any other title; adding an excalamation mark to it to compete for attention is a form of defection in a prisoner's dilemma.2012-11-23
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    sure. thanks for advicing, joriki. I will try to make the question better.2012-11-23
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    the question has been modified... hope this time could give all of you a clear picture of it. Feel comfortable to point out any mistake in it. Thanks!2012-11-23

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