Selling to a principal and a budget-constrained agent

TL;DR

This paper characterizes optimal selling mechanisms when selling to a principal-agent pair with different valuations and a budget constraint, revealing a threshold-based mechanism design involving posted prices and randomization.

Contribution

It introduces a model with a budget-constrained agent and a principal, deriving the revenue-maximizing mechanism in a two-dimensional type space with novel threshold-based strategies.

Findings

Below a budget threshold, a mechanism with two posted prices and randomization is optimal.

Above the threshold, a simple single posted price mechanism is optimal.

The model captures strategic delegation and valuation differences in principal-agent settings.

Abstract

We analyze a model of selling a single object to a principal-agent pair who want to acquire the object for a firm. The principal and the agent have different assessments of the object's value to the firm. The agent is budget-constrained while the principal is not. The agent participates in the mechanism, but she can (strategically) delegate decision-making to the principal. We derive the revenue-maximizing mechanism in a two-dimensional type space (values of the agent and the principal). We show that below a threshold budget, a mechanism involving two posted prices and three outcomes (one of which involves randomization) is the optimal mechanism for the seller. Otherwise, a single posted price mechanism is optimal.