<p>Consider the following extensive-form game:</p>
<p><a href="https://i.sstatic.net/VazMY.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/VazMY.png" alt="enter image description here" /></a></p>
<p>In one alternative, Player 2 chooses G and E and Player 1 chooses D. However, Player 2 can increase her gain by making a credible threat and switch from G to H, prompting Player 1 to play C.</p>
<p>Are credible threats accounted for in the SPNE / backward induction framework? Would (D, {E, G}) be considered a subgame perfect equilibrium? How many subgame perfect equilibria are there in this game?</p>

CC BY-SA 4.0
2021-12-11T23:37:31.947Z
Do you know the definition of SPE? If yes, where is it unclear how to apply it here?
Michael Greinecker
CC BY-SA 4.0
2021-12-11T23:43:16.697Z
@MichaelGreinecker I believe that I know the formal definition of SPNE and that (D, {E, G}) would satisfy it. However, what confuses me is that SPNE was developed in order to refine Nash Equilibria and exclude non-credible threats. But it seems that in doing so credible threats were excluded too. If that’s the case, is there a further refinement / extension of SPNEs that allows for credible threats?
GingerBadger
CC BY-SA 4.0
2021-12-11T23:54:09.113Z
You are right, (D, {E, G}) is a SPE. This game has actually a continuum of SPE. The meaning of  "threat" is somewhat ambiguous. If player 2 could announce some threat, in the beginning, that could be made part of the game.  But then it is not part of the solution concept. Note also that your game is extremely special. If you slightly change the payoffs, you end up with a unique SPE. Only payoff-ties allow here for multiple SPE.
Michael Greinecker
CC BY-SA 4.0
2021-12-12T01:53:05.010Z
Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.
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<game-theory><nash-equilibrium><extensive-games>
Does Subgame Perfect Nash Equilibria (SPNE) allow for credible threats?
GingerBadger
# Does Subgame Perfect Nash Equilibria (SPNE) allow for credible threats?

(Asked by: username_0 on 2021-12-11)

Consider the following extensive-form game:

[![enter image description here](https://i.sstatic.net/VazMY.png)](https://i.sstatic.net/VazMY.png)

In one alternative, Player 2 chooses G and E and Player 1 chooses D. However, Player 2 can increase her gain by making a credible threat and switch from G to H, prompting Player 1 to play C.

Are credible threats accounted for in the SPNE / backward induction framework? Would (D, {E, G}) be considered a subgame perfect equilibrium? How many subgame perfect equilibria are there in this game?

**Tags:** game-theory, nash-equilibrium, extensive-games

> **Comments:**
> **username_1**: Do you know the definition of SPE? If yes, where is it unclear how to apply it here?  
> **username_0**: @username_1 I believe that I know the formal definition of SPNE and that (D, {E, G}) would satisfy it. However, what confuses me is that SPNE was developed in order to refine Nash Equilibria and exclude non-credible threats. But it seems that in doing so credible threats were excluded too. If that’s the case, is there a further refinement / extension of SPNEs that allows for credible threats?  
> **username_1**: You are right, (D, {E, G}) is a SPE. This game has actually a continuum of SPE. The meaning of  "threat" is somewhat ambiguous. If player 2 could announce some threat, in the beginning, that could be made part of the game.  But then it is not part of the solution concept. Note also that your game is extremely special. If you slightly change the payoffs, you end up with a unique SPE. Only payoff-ties allow here for multiple SPE.  
> **username_2**: Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking.  

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## 0 answers

