Revenue-Optimal Efficient Mechanism Design with General Type Spaces

TL;DR

This paper develops a comprehensive framework for designing revenue-optimal, efficient mechanisms in complex multi-dimensional settings with arbitrary informational constraints, expanding the scope of prior models.

Contribution

It introduces a novel characterization of optimal mechanisms using network flow structures applicable to general type spaces, surpassing previous limitations.

Findings

Provides a new characterization of optimal mechanisms based on allocations and connected components.

Utilizes network flow structures to analyze complex informational constraints.

Significantly broadens the types of agent information that can be incorporated into mechanism design.

Abstract

We derive the revenue-optimal efficient (welfare-maximizing) mechanism in a general multidimensional mechanism design setting when type spaces -- that is, the underlying domains from which agents' values come from -- can capture arbitrarily complex informational constraints about the agents. Type spaces can encode information about agents representing, for example, machine learning predictions of agent behavior, institutional knowledge about feasible market outcomes (such as item substitutability or complementarity in auctions), and correlations between multiple agents. Prior work has only dealt with connected type spaces, which are not expressive enough to capture many natural kinds of constraints such as disjunctive constraints. We provide two characterizations of the optimal mechanism based on allocations and connected components; both make use of an underlying network flow structure to the mechanism design. Our results significantly generalize and improve the prior state of the art in revenue-optimal efficient mechanism design. They also considerably expand the scope of what forms of agent information can be expressed and used to improve revenue.