# Mechanism Design and Multidimensional Type Spaces

Is it possible to design a mechanism of agents with multidimensional types?

In particular, what if the type space has the following form: $$\Theta_i=\{\theta_i\in\{{1,2,\dots, n}\}\times[0,1]:n\in\mathbb{N}\}.$$

So far, in my search, I haven't found any such example. Most papers either deal with discrete or continuous multidimensional types.

I'd appreciate any help or references. Thank you.

• Is it of great importance that the part in [0,1] covers the whole interval? You could discretize it with tiny steps $[0,\epsilon,2\epsilon,...,1]$ and build on the papers with discrete type spaces. In any case, I am not aware of such a paper. I suggest you check who is citing McAfee&McMillan, JET 1988, and see if something pops up. – Bayesian Sep 10 '20 at 9:02