Delegation with Discreteness 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?
I believe this is the basic case discussed in the Laffont-Martimort textbook "The Theory of Incentives". The choice of the agent is either 0 or 1. You can find a complete description in "The Moral Hazard" chapter, section 4.2. The results are listed later, and while I am not sure, I do not think there should be qualitative differences.