Interdependent Bilateral Trade: Information vs Approximation

TL;DR

This paper explores welfare maximization in bilateral trade with interdependent values, classifying information structures to determine where approximation mechanisms can be effectively designed.

Contribution

It introduces a classification of information structures based on private signal influence and analyzes the feasibility of approximation mechanisms in interdependent settings.

Findings

Identifies conditions under which welfare approximations are possible.

Classifies information structures by influence levels.

Analyzes approximation ratios for specific information families.

Abstract

Welfare maximization in bilateral trade has been extensively studied in recent years. Previous literature obtained incentive-compatible approximation mechanisms only for the private values case. In this paper, we study welfare maximization in bilateral trade with interdependent values. Designing mechanisms for interdependent settings is much more challenging because the values of the players depend on the private information of the others, requiring complex belief updates and strategic inference. We propose to classify information structures by quantifying the influence that a player's private signal has on their own valuation. We then paint a picture of where approximations are possible and impossible based on these information structures. Finally, we also study the possible approximation ratios for a natural family of information structures.