<p>The original problem solved by Rubinstein (bargaining on infinite horizon with fixed discounts) is sufficiently clear to me but I can't understand what will happen in the following situation.</p>
<p>Suppose, two players make offers to each other. The Player 1 makes an offer in periods 3k+1, the Player 2 in 3k+3 and in the 3k+2 no one makes an offer (where k = 0, 1, 2...).  So, for Player 2 there is an increased discount for declining offer.</p>
<p>Supposing equal discount factors for players 1 and 2, I've thought that the solution would've been: Player 1 offers to Player 2</p>
<p><span class="math-container">$$
s_1 = \frac{d(1-d)}{1-d^3}
$$</span></p>
<p>but that doesn't seem to be correct...</p>
<p>In general my question is how would the SPE solution of the original bargaining game change in case there is an extra period that only affects one player?</p>

CC BY-SA 4.0
2024-06-01T22:23:54.753Z
Why should the additional period only affect one player?
Michael Greinecker
CC BY-SA 4.0
2024-06-01T23:15:17.197Z
Hi @MichaelGreinecker! That was my assumption, it might have been wrong..

My logic was as follows: if in 3k+1 if Player 2 declines, his payoff in 3k+3 will be d^2*v. If the Player 1 declines, his payoff in the next stage will be d^3*v (he doesn't have to wait extra period to make an offer). Is it not correct?
Feelings.сfg
CC BY-SA 4.0
2024-06-02T11:46:08.897Z
If I decline in this period, don't I have to wait out both the period in which you get to make an offer and the fallow period anyway (regardless of whether I'm the first or second player).
matthewoulton
<game-theory><dynamic-games><bargaining>
Bargaining on infinite horizon with no offer period
Feelings.сfg
# Bargaining on infinite horizon with no offer period

(Asked by: username_0 on 2024-06-01)

The original problem solved by Rubinstein (bargaining on infinite horizon with fixed discounts) is sufficiently clear to me but I can't understand what will happen in the following situation.

Suppose, two players make offers to each other. The Player 1 makes an offer in periods 3k+1, the Player 2 in 3k+3 and in the 3k+2 no one makes an offer (where k = 0, 1, 2...). So, for Player 2 there is an increased discount for declining offer.

Supposing equal discount factors for players 1 and 2, I've thought that the solution would've been: Player 1 offers to Player 2

$$
s\_1 = \frac{d(1-d)}{1-d^3}
$$

but that doesn't seem to be correct...

In general my question is how would the SPE solution of the original bargaining game change in case there is an extra period that only affects one player?

**Tags:** game-theory, dynamic-games, bargaining

> **Comments:**
> **username_1**: Why should the additional period only affect one player?  
> **username_0**: Hi @username_1! That was my assumption, it might have been wrong..  My logic was as follows: if in 3k+1 if Player 2 declines, his payoff in 3k+3 will be d^2*v. If the Player 1 declines, his payoff in the next stage will be d^3*v (he doesn't have to wait extra period to make an offer). Is it not correct?  
> **username_2**: If I decline in this period, don't I have to wait out both the period in which you get to make an offer and the fallow period anyway (regardless of whether I'm the first or second player).  

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## 0 answers

