Is this premise on iterated knowledge too restrictive for fruitful applications?

Question

I want to play around with a model for iterated knowledge which I kind of made up, but I it contains a premise of which I don't know whether it is practical.

I basically assumed that it makes no difference if

• agent $a$ assigns probability $p$ to the fact that agent $b$ assigns probability $q$ to some event $E$

• or $a$ assigns probability $pq$ to the fact that $b$ assigns probability $1$ to $E$.

So particularly one can swap $p$ with $q$ in that situation.

Is it worthwhile to further explore this setting or is the assumption too restrictive for fruitful applications?

Answer 1

If your application is to game theory, as your tag suggest, such a model is not very useful.The problem is that itmight be the case that a certain action is optimal for agent $b$ if and only if the probability she assigns to $E$ is at least $r$ for $q<r<1$, then the probability of doing the action differs in the two settings.