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Revenue-Optimal Efficient Mechanism Design with General Type Spaces

Siddharth Prasad, Maria-Florina Balcan, Tuomas Sandholm

TL;DR

The paper addresses revenue-optimal efficient mechanism design when agent type spaces are general and possibly disconnected, where WT can be suboptimal. It develops two equivalent characterizations—the allocation-wise Groves and the component-wise Groves—both supported by a novel network-flow formulation that captures incentive compatibility and individual rationality constraints. The authors show that the revenue-optimal mechanism is unique within these classes and can be computed via shortest-path problems on induced graphs, connecting allocation partitions or connected components to payments. This generalizes beyond connected-type results, broadening the expressive power of agent information (e.g., exclusivity, conditionals, discrete types) and offering a foundation for practical, data-driven design of pricing rules in complex markets.

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.

Revenue-Optimal Efficient Mechanism Design with General Type Spaces

TL;DR

The paper addresses revenue-optimal efficient mechanism design when agent type spaces are general and possibly disconnected, where WT can be suboptimal. It develops two equivalent characterizations—the allocation-wise Groves and the component-wise Groves—both supported by a novel network-flow formulation that captures incentive compatibility and individual rationality constraints. The authors show that the revenue-optimal mechanism is unique within these classes and can be computed via shortest-path problems on induced graphs, connecting allocation partitions or connected components to payments. This generalizes beyond connected-type results, broadening the expressive power of agent information (e.g., exclusivity, conditionals, discrete types) and offering a foundation for practical, data-driven design of pricing rules in complex markets.

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.
Paper Structure (20 sections, 9 theorems, 12 equations, 1 figure)

This paper contains 20 sections, 9 theorems, 12 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Our Contributions
  3. Related Work
  4. Mechanism Design with Complex Type Spaces
  5. Weakest Types
  6. Revenue-Maximizing Mechanism Design Without an Efficiency Constraint
  7. Problem Formulation, Mechanism Design Background, and Examples of Disconnected Type Spaces
  8. Type Spaces
  9. Efficiency, Incentive Compatibility, and Individual Rationality
  10. Groves Mechanisms and Weakest Types
  11. Optimal Efficient Mechanism Design with Connected Type Spaces
  12. Examples of Disconnected Type Spaces
  13. Example Illustrating Sub-optimality of Vanilla Weakest Type
  14. Characterization of the Optimal Efficient Mechanism
  15. Allocational Characterization of the Optimal Efficient Mechanism
  16. ...and 5 more sections

Key Result

Theorem 2.1

Suppose $\Theta_i(\bm{v}_{-i})$ is connected for every $\bm{v}_{-i}$. Let $\bm{p}$ be an IC pricing rule and let $\bm{p}'$ be any other pricing rule. Then, $\bm{p}'$ is IC if and only if there exist functions $h_i : \boldsymbol{\Theta}_{-i}\to\mathbb{R}$ such that $p_i'(\bm{v}) = p_i(\bm{v})+h_i(\bm

Figures (1)

  • Figure 1: Examples of a disconnected type space $\Theta_1 = \Theta_1^A\cup\Theta_1^B$ and the corresponding graph $G$ encoding the optimal efficient mechanism. The solid edges in $G$ make up the tree of shortest paths.

Theorems & Definitions (15)

  • Theorem 2.1: Revenue Equivalence Green77:CharacterizationHolmstroem79:Groves
  • Theorem 2.2: Uniqueness of Groves Mechanisms Green77:CharacterizationHolmstroem79:Groves
  • Theorem 2.3: Optimality of Weakest Type krishna1998efficientbalcan2023bicriteria
  • Lemma 4.1
  • proof
  • Theorem 4.2
  • proof
  • Theorem 4.3
  • proof : Proof of Theorem \ref{['thm:allocational-characterization']}
  • Lemma 4.4
  • ...and 5 more