# Why Sequenial Equilibrium (SE) imposes no restrictions on the off-equilibrium beliefs in the Spence's model?

I read some lectures on the Spence's model. Some (see e.g. P31 of lecture 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.

• 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. Jan 22 at 22:10
• @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? Jan 23 at 6:04
• You can allow more levels, but only finitely many. Jan 23 at 7:55
• @Michael Greinecker Do you know any formal references or examples about discretizing the action space in signaling games? Thanks. Jan 23 at 8:09
• 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. Jan 23 at 8:56