TTC Domains

2025-01-26

AI Summary

This paper characterizes the “TTC domain”—the maximal preference domain over objects under strict preferences where the Top Trading Cycles (TTC) mechanism is the unique rule satisfying individual rationality, Pareto efficiency, and strategy-proofness. We introduce a sufficient condition for TTC-domain membership—the “Top-Two Condition”—and derive its necessary weakening for the three-object case, thereby achieving the first complete characterization of the TTC domain with three objects. Our framework unifies classical domains such as single-peaked and single-valley preferences, exposing their shared structural properties. Furthermore, we systematically evaluate several novel preference domains to determine TTC-domain membership, clarifying the fundamental boundaries of TTC’s applicability. These results provide foundational conceptual tools and methodological support for domain-restriction theory in mechanism design.

Technology Category

• Knowledge Representation and Reasoning: Preferences
• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We study the classical object reallocation problem under strict preferences, with a focus on characterizing"TTC domains"-- preference domains on which the Top Trading Cycles (TTC) mechanism is the unique mechanism satisfying individual rationality, Pareto efficiency, and strategyproofness. We introduce a sufficient condition for a domain to be a TTC domain, which we call the top-two condition. This condition requires that, within any subset of objects, if two objects can each be most-preferred, they can also be the top-two most-preferred objects (in both possible orders). A weaker version of this condition, applying only to subsets of size three, is shown to be necessary. These results provide a complete characterization of TTC domains for the case of three objects, unify prior studies on specific domains such as single-peaked and single-dipped preferences, and classify several previously unexplored domains as TTC domains or not.

Problem

• Object Reallocation
• Top Trading Cycles
• Mechanism Design

Innovation

• Top-two Condition
• TTC Domains
• Object Reallocation