Envy Cycle Elimination with Strategic Agents: Best Responses and Fairness Guarantees
This work addresses the behavior of a widely used fair division algorithm under strategic agent behavior, which is a critical consideration for practical applications involving self-interested participants. It is an incremental step in understanding the robustness of fair division mechanisms.
This paper investigates the Envy Cycle Elimination (E-C-E) procedure when agents act strategically, revealing that incentives complicate its execution significantly. Despite these challenges, the authors provide the first results on the existence of Pure Nash Equilibria for various E-C-E versions and demonstrate that some versions approximately preserve fairness guarantees for agents playing best responses.
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.