<p>Consider a sequential game with two players who use the following procedure to share two desirable, identical and indivisible objects. Player 1 proposes an allocation in stage 1 which player 2 either accepts or rejects. In the event of rejection, neither player receives either of the objects and in the event of acceptance the objects are allocated according to the proposal of player 1.</p>

<p>The subgame perfect Nash equilibrium of the game is where player 1 allocates both the objects to himself and player 2 receives nothing. Is there any Nash equilibrium of this game other this?</p>

CC BY-SA 3.0
2017-05-06T06:48:40.077Z
Hint: "player 2 receives nothing" only refers to the outcome, but what exactly is her strategy? This has implications on what player 1 would optimally propose in the first stage.
Herr K.
CC BY-SA 3.0
2017-05-06T07:15:24.080Z
[Ultimatum game](https://en.wikipedia.org/wiki/Ultimatum_game)
Henry
CC BY-SA 3.0
2017-05-06T07:47:15.570Z
@HerrK. Player 2's strategy is whatever player 1 allocates, she will accept that. But still I couldn't figure out if there is any other NE
QED
CC BY-SA 3.0
2017-05-06T18:00:08.880Z
@AbishankaSaha Accepting regardless of player 1's proposal is not the only strategy available to player 2. Consider scenarios in which player 2 rejects 1's proposal
Herr K.
<game-theory>
Sequential Bargaining
QED
# Sequential Bargaining

(Asked by: username_0 on 2017-05-06)

Consider a sequential game with two players who use the following procedure to share two desirable, identical and indivisible objects. Player 1 proposes an allocation in stage 1 which player 2 either accepts or rejects. In the event of rejection, neither player receives either of the objects and in the event of acceptance the objects are allocated according to the proposal of player 1.

The subgame perfect Nash equilibrium of the game is where player 1 allocates both the objects to himself and player 2 receives nothing. Is there any Nash equilibrium of this game other this?

**Tags:** game-theory

> **Comments:**
> **username_1**: Hint: "player 2 receives nothing" only refers to the outcome, but what exactly is her strategy? This has implications on what player 1 would optimally propose in the first stage.  
> **username_2**: [Ultimatum game](https://en.wikipedia.org/wiki/Ultimatum_game)  
> **username_0**: @HerrK. Player 2's strategy is whatever player 1 allocates, she will accept that. But still I couldn't figure out if there is any other NE  
> **username_1**: @AbishankaSaha Accepting regardless of player 1's proposal is not the only strategy available to player 2. Consider scenarios in which player 2 rejects 1's proposal  

---

## 0 answers

