The influence of restricted type space on incentive compatible mechanism design?
The type space is the support of the belief about the types. It seems a bit weird to allow a mechanism designer to arbitrarily restrict their belief support. However, you are right: if the designer can find out more about the private types by acquiring information, this would intuitively allow them to reduce information rent, because it makes the type &quot;less private.&quot; Of course it would be best to fully unveil types such that no incentive for revelation has to be provided and full surplus extraction becomes possible. In your constructed example it may not be helpful to exclude very high types $&gt;M$ as more profitable deviations are often found in closer vicinity to the real type. That depends on the problem at hand of course.
I can't see clearly where you want to go with this. So let me suggest something else in a similar spirit: mechanism design with evidence. Here, agents can make their private information hard by providing evidence that their true type belongs to some subset of the type space. See, e.g., the work by Ben-Porath, Dekel &amp; Lipman (AER 2014, Ecta 2019 and more), Bull and Watson (GEB 2007), Hagenbach, Koessler &amp; Perez-Richet (Ecta 2014) and others.