# Existence of solutions to principal-agent problems with adverse selection under minimal assumptions

## TL;DR

This paper establishes an existence theorem for principal-agent problems with adverse selection under broad conditions, relaxing traditional assumptions on the spaces involved and accommodating more complex models.

## Contribution

It introduces a general coercivity condition that replaces finite-dimensional or compact assumptions, enabling broader applicability of existence results in principal-agent models.

## Key findings

- Proves existence of solutions under minimal assumptions
- Flexible approach adaptable to partial participation models
- Handles type-dependent budget constraints

## Abstract

We prove an existence result for the principal-agent problem with adverse selection under general assumptions on preferences and allocation spaces. Instead of assuming that the allocation space is finite-dimensional or compact, we consider a more general coercivity condition which takes into account the principal's cost and the agents' preferences. Our existence proof is simple and flexible enough to adapt to partial participation models as well as to the case of type-dependent budget constraints.