Selling two complementary goods

TL;DR

This paper characterizes optimal selling mechanisms for a seller offering two divisible complementary goods to an agent with private information, showing that simple posted price mechanisms are often optimal under certain distribution assumptions.

Contribution

It provides a complete characterization of incentive constraints and demonstrates that posted price mechanisms are optimal in various distribution settings for selling complementary goods.

Findings

Optimal mechanisms are ratio-dependent posted prices.

Posted prices are optimal when value and ratio are independent.

The model applies to a two-dimensional private information setting.

Abstract

A seller is selling a pair of divisible complementary goods to an agent. The agent consumes the goods only in a specific ratio and freely disposes of excess in either goods. The value of the bundle and the ratio are private information of the agent. In this two-dimensional type space model, we characterize the incentive constraints and show that the optimal (expected revenue-maximizing) mechanism is a ratio-dependent posted price or a posted price mechanism for a class of distributions. We also show that the optimal mechanism is a posted price mechanism when the value and the ratio are independently distributed.