How to intuitively understand the 'Intuitive criterion'? The intuitive criterion by Cho and Kreps is a refinement to minimise the set of perfect Bayesian equilibria in signalling games. What would a simple and intuitive example to explain this criterion be? Assume any undergrad student should be easily able to appreciate the refinement through the example.
A concise, completely informal way of putting it is this: The intuitive criterion rules-out any out-of-equilibrium beliefs that can only be correct if some player did something stupid.
Below is a slightly more long-winded explanation with an informal example.

In many signalling games (that is, games in which one player—the sender—can communicate information to another—the receiver), there are often a lot of implausible equilibria. This happens because the Perfect Bayesian solution concept does not specify what the receiver's beliefs must be when the sender deviates; we can therefore support a lot of equilibria simply by saying that if the sender deviates from those equilibria then he will be &quot;punished&quot; with very bad beliefs. Such punishment will usually be enough to make the sender play a strategy that would otherwise not be a best response.
For example, in Spence's classic job market signalling paper there is an equilibrium in which high-ability individuals invest in education (learning is easy for them) whilst low-ability individuals do not (because they find it too costly to do so). Education is then a signal of ability. We might ask: is there also an equilibrium of this game in which nobody chooses to get an education and no information is transmitted to the receiver? The answer is 'yes'. We can support such an equilibrium by saying that a deviation in which a sender is educated causes the receiver to adopt the belief that the sender is certainly low-ability. If education has the effect of signalling low-ability then, of course, everyone is happy to play along with the putative equilibrium and not get educated.
It is also clear that this equilibrium is not very plausible: the receiver knows that it is less costly for a high-ability agent to get an education than a low-ability one, so it doesn't make much sense for him to think of an education as signalling low-ability. The intuitive criterion rules out this kind of equilibrium by requiring beliefs to be &quot;reasonable&quot; in the following sense:

Suppose the receiver observes a deviation from the equilibrium. The receiver should not believe that the sender is of type $t_{\text{bad}}$ if both of the following are true:

the deviation would result in
type $t_{\text{bad}}$ being worse off then if he has stuck to the equilibrium for any beliefs.
there is some type $t_{\text{good}}$ who is better off by playing the deviation than by sticking to the equilibrium for some belief other than $t_{\text{bad}}$.


Returning to the education signalling model: Suppose that the equilibrium is that nobody gets an education and that the receiver believes that a deviation to getting education signals low ability. Anticipating these beliefs, a low ability worker is made worse-off by deviating because he not only incurs the cost of the education but is then thought of as a bad type as a result. Thus, condition 1. is satisfied.
Can we find some alternative belief such that the high-ability worker would like to deviate to getting education? The answer is yes: if the receiver believes that education signals high ability then this deviation is indeed profitable for the high-type. Thus, condition 2 is also satisfied.
Since both conditions are satisfied, the intuitive criterion rules-out the implausible pooling equilibrium.