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.


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