Envy Cycle Elimination with Strategic Agents: Best Responses and Fairness Guarantees

2026-05-29

AI Summary

This study investigates the fairness guarantees and equilibrium properties of the envy-cycle elimination (E-C-E) mechanism in settings with strategic agents. Addressing the challenge of potential manipulation by self-interested participants, we formulate a game-theoretic model to analyze how natural variants of the E-C-E mechanism influence strategic interactions. Employing tools from mechanism design and game theory, we provide the first characterization of the complexity inherent in applying E-C-E under strategic behavior. Our main contributions include introducing several intuitive mechanism variants, proving that some admit pure-strategy Nash equilibria, and demonstrating that approximate EF1 fairness is preserved at equilibrium. These results offer theoretical foundations for designing fair allocation mechanisms robust to strategic manipulation.

Abstract

With strong evidence in the literature showing that fairness and truthfulness are incompatible, there is a recent line of work focusing on the fairness properties of equilibria of simple fair division mechanisms, especially Round-Robin. We consider the Envy Cycle Elimination (E-C-E) procedure of Lipton et al. [23], one of the most versatile tools in fair division. While this simple and intuitive algorithm achieves allocations that are envy-free up to one item (EF1) for any number of agents and general monotone valuation functions, surprisingly little is known about its behavior when agents act strategically. We demonstrate how the presence of incentives, although highly natural and relevant for the majority of applications, completely removes the intuitive clarity in the algorithm's execution, even for a few agents and very simple valuation functions. Additionally, while in the standard algorithmic setting there is great flexibility in how the details of E-C-E are implemented, here additional specifications are needed before the procedure is clearly defined, the choice of which has a potentially huge impact on the agents' behavior. Despite these obstacles, for various natural versions of E-C-E, we give the first results on the existence of Pure Nash Equilibria of the resulting mechanisms, and show there exist versions where fairness guarantees are approximately preserved for agents who play best responses.

Problem

• strategic agents
• fair division
• envy cycle elimination
• truthfulness
• fairness guarantees

Innovation

• Envy Cycle Elimination
• Strategic Agents
• Pure Nash Equilibrium
• EF1 Fairness
• Best Response