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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.

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

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