Choi and Li Prove Temporal Fair Division Possible with New Algorithm

Choi and Li’s work tackles the challenge of allocating indivisible goods over time while ensuring cumulative fairness. They define Temporal Envy-Freeness Up to Any Good (TEFX) and Temporal Maximin Share (TMMS) — dynamic extensions of classic static fairness criteria. Since these strict notions are generally impossible, the authors systematically analyze structured constraints (e.g., strong binary valuations, identical valuations, bi-valued goods) to map exactly where temporal fairness is achievable and where it is not. Their key technical contribution is a dynamic backtracking algorithm that achieves exact TEFX for agents with strong binary valuations. The algorithm uses bounded historical reallocation and a lexicographical potential function to resolve temporal envy cycles, guaranteeing finite termination.

Beyond the exact result, the paper delivers tight approximation ratios for α-TEFX under identical valuations and bi-valued goods, as well as definitive impossibility proofs for TEFX and TMMS in broader settings. This work contextualizes prior algorithms that implicitly satisfied the newly defined TMMS metric, showing where they fall short. Accepted to the International Symposium on Algorithmic Game Theory (SAGT) 2026, the research provides a rigorous foundation for fair sequential resource allocation. Practical implications range from cloud computing job scheduling to AI training data distribution over time, where fairness guarantees across rounds are critical.