often not within the class of mechanisms being searched over.

The second approach forgoes structures that are easily interpretable, and exhaustively searches for the optimal mechanism. This is exemplified by solving mathematical programs (typically linear or convex programs) whose feasible regions contain the set of all incentive compatible mechanisms (see, e.g. [@conitzer2002complexity]; [@DFK15]; [@DDT17];[@FH18]). Typically, incentive requirements are hardwired as constraints in such programs.

Difficulty arises in the second approach when one would like to adopt strong incentive guarantees such as DSIC, which need at least one constraint per profile of types to specify. When the space of possible types is a continuum, this gives rise to uncountably many constraints. While this does not always make the program impossible to solve it considerably complicates the task. One way to work around this is to discretize the type space and only impose incentive compatible (IC) constraints on the set of discrete types used to represent the type space. Discretization is also embodied in the idea of a given prior distribution over a set of discrete types, on which the optimization can then be based (e.g. [@conitzer2002complexity]; [@DFK15]). The most common motivation for such prior distributions is that they naturally result from 