Adjusted Winner: from Splitting to Selling

2026-02-12

AI Summary

This work addresses the practical limitations of the traditional Adjusted Winner mechanism, which relies on divisible resource allocation and is thus ill-suited for indivisible goods. The authors propose a novel mechanism that incorporates partial market transactions—allowing some items to be sold under a budget constraint—and redistributes the proceeds among agents. This approach uniquely integrates market-based exchange and equitable redistribution within the Adjusted Winner framework. The problem is formalized as a combinatorial optimization task, proven to be NP-hard, and solved via a fully polynomial-time approximation scheme (FPTAS). Axiomatic analysis confirms that the mechanism satisfies key fairness properties, including envy-freeness. Experimental simulations demonstrate that the proposed method significantly enhances practical feasibility while maintaining high levels of fairness.

Technology Category

• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

The Adjusted Winner (AW) method is a fundamental procedure for the fair division of indivisible resources between two agents. However, its reliance on splitting resources can lead to practical complications. To address this limitation, we propose an extension of AW that allows the sale of selected resources under a budget constraint, with the proceeds subsequently redistributed, thereby aiming for allocations that remain as equitable as possible. Alongside developing this extended framework, we provide an axiomatic analysis that examines how equitability and envy-freeness are modified in our setting. We then formally define the resulting combinatorial problems, establish their computational complexity, and design a fully polynomial-time approximation scheme (FPTAS) to mitigate their inherent intractability. Finally, we complement our theoretical results with computer-based simulations.

Problem

• fair division
• indivisible resources
• Adjusted Winner
• budget constraint
• equitability

Innovation

• Adjusted Winner
• fair division
• indivisible goods
• budget-constrained selling
• FPTAS