<p>I read some lectures on the Spence's model. Some (see e.g. P31 of <a href="https://ocw.mit.edu/courses/economics/14-16-strategy-and-information-spring-2016/lecture-slides/MIT14_16S16_equilib_refine.pdf" rel="nofollow noreferrer">lecture</a> PPT from MIT game thoery course) mention that SE imposes no restrictions on the off-equilibrium beliefs but without proof. I am wondering how they get that result because to me, I think verifying an equilibrium in the Spence model is an SE should be difficult since the message space of the worker is continuous.</p>

CC BY-SA 4.0
2022-01-22T22:10:49.193Z
I guess the statement refers to a version of Spence's model with discrete effort levels, at least by analogy. There simply is no sequential equilibrium as usually defined with a continuum of possible effort levels.
Michael Greinecker
CC BY-SA 4.0
2022-01-23T06:04:16.367Z
@Michael Greinecker Oh, that means if we denote the equilibrium education level sent by the worker in a pooling equilibrium as $e^{*}$, then the message space of the worker in that pooling can be viewed as $\{ e^{*}, \text{not}\, e^{*} \}$, right?
DevinY
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2022-01-23T07:55:50.540Z
You can allow more levels, but only finitely many.
Michael Greinecker
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2022-01-23T08:09:26.723Z
@Michael Greinecker Do you know any formal references or examples about discretizing the action space in signaling games? Thanks.
DevinY
CC BY-SA 4.0
2022-01-23T08:56:39.883Z
None comes to mind, but I'm sure I have seen it in some textbooks before. The argument why there is no additional restriction on off equilibrium beliefs is not that hard though.
Michael Greinecker
<game-theory><nash-equilibrium><dynamic-games><equilibrium-selection>
Why Sequenial Equilibrium (SE) imposes no restrictions on the off-equilibrium beliefs in the Spence's model?
DevinY
# Why Sequenial Equilibrium (SE) imposes no restrictions on the off-equilibrium beliefs in the Spence's model?

(Asked by: username_0 on 2022-01-21)

I read some lectures on the Spence's model. Some (see e.g. P31 of [lecture](https://ocw.mit.edu/courses/economics/14-16-strategy-and-information-spring-2016/lecture-slides/MIT14_16S16_equilib_refine.pdf) PPT from MIT game thoery course) mention that SE imposes no restrictions on the off-equilibrium beliefs but without proof. I am wondering how they get that result because to me, I think verifying an equilibrium in the Spence model is an SE should be difficult since the message space of the worker is continuous.

**Tags:** game-theory, nash-equilibrium, dynamic-games, equilibrium-selection

> **Comments:**
> **username_1**: I guess the statement refers to a version of Spence's model with discrete effort levels, at least by analogy. There simply is no sequential equilibrium as usually defined with a continuum of possible effort levels.  
> **username_0**: @username_1 Oh, that means if we denote the equilibrium education level sent by the worker in a pooling equilibrium as $e^{*}$, then the message space of the worker in that pooling can be viewed as $\{ e^{*}, \text{not}\, e^{*} \}$, right?  
> **username_1**: You can allow more levels, but only finitely many.  
> **username_0**: @username_1 Do you know any formal references or examples about discretizing the action space in signaling games? Thanks.  
> **username_1**: None comes to mind, but I'm sure I have seen it in some textbooks before. The argument why there is no additional restriction on off equilibrium beliefs is not that hard though.  

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## 0 answers

