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Selling to a principal and a budget-constrained agent

Debasis Mishra, Kolagani Paramahamsa

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.

Selling to a principal and a budget-constrained agent

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.
Paper Structure (19 sections, 80 equations, 6 figures)

This paper contains 19 sections, 80 equations, 6 figures.

Table of Contents

  1. Introduction
  2. An illustration
  3. Layout of the paper
  4. The model
  5. Optimal mechanism
  6. Description of optimal post-2 mechanisms
  7. Relation to the literature
  8. Discussions
  9. Proof of Lemma \ref{['lem:post2']}
  10. Proof of Theorem \ref{['theo:main']}
  11. post-2 is optimal in $M^+$
  12. Upper bounding $V_{\ell}$
  13. Upper bounding $V_h$
  14. Upper bounding $V_m$ and proof of Theorem \ref{['theo:main']}
  15. post-1 is optimal in $M^-$
  16. ...and 4 more sections

Figures (6)

  • Figure 1: Illustration of new IC mechanisms
  • Figure 2: A post-2 mechanism
  • Figure 3: Partitioning of type space $V$
  • Figure 4: Optimal mechanism in $M^{\ell}$ for type space $V_{\ell}$
  • Figure 5: Optimal mechanism in $M^{h}$ for type space $V_h$
  • ...and 1 more figures