Existence in Multidimensional Screening with General Nonlinear Preferences

TL;DR

This paper proves the existence of solutions in multidimensional screening problems with complex nonlinear preferences using advanced convex analysis techniques.

Contribution

It extends previous work by providing an existence proof for general nonlinear preferences in multidimensional screening.

Findings

Established existence of solutions under broad nonlinear preferences

Utilized $G$-convex analysis to handle complex constraints

Generalized prior models to more realistic preference structures

Abstract

We generalize the approach of Carlier (2001) and provide an existence proof for the multidimensional screening problem with general nonlinear preferences. We first formulate the principal's problem as a maximization problem with $G$-convexity constraints and then use $G$-convex analysis to prove existence.