# Mechanism design when the set of feasible decisions depends on types

Q : Can the tools of mechanism design be applied when the set of feasible decisions $$D$$ depends on the types $$\theta$$?

For example, when $$d \in D$$ represents the total funding allocated toward some good and $$\theta_i$$ represents the funds $$i$$ has available, $$D = \{ d | 0 < d < \sum\limits_i\theta_i\}$$.

Q : If not, is there some other approach that analyzes this sort of scenario?