How to Make Envy Vanish Over Time
نویسنده
چکیده
We study the dynamic fair division of indivisible goods. Suppose T items arrive online and must be allocated upon arrival to one of n agents, each of whom has a value in [0, 1] for the current item. Our goal is to design allocation algorithms that minimize the maximum envy at time T , EnvyT , dened as the maximum dierence between any agent’s overall value for items allocated to another agent and to herself. We say that an algorithm has vanishing envy if the ratio of envy over time, EnvyT /T , goes to zero as T goes to innity. We design a polynomial-time, deterministic algorithm that achieves EnvyT ∈ Õ( √ T /n), and show that this guarantee is asymptotically optimal. We also derive tight (in T ) bounds for a more general seing where items arrive in batches.
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