Consider a game of delegation. An uninformed principal must delegate some task to an informed agent with preferences imperfectly aligned.
I'm aware of plenty of literature that studies these kinds of problems when there is a continuous action space, Alonso and Matouschek (2008) for example. Their lit review also seems to feature papers with continuous spaces. Quadratic loss utilities are very popular.
Are there any papers featuring delegation of a decision which is constrained to some discrete space? Do qualitative results change?