We study the allocation of shared resources over multiple rounds among competing agents, via a dynamic max-min fair (DMMF) mechanism: the good in each round is allocated to the requesting agent with the least number of allocations received to date. Previous work has shown that when an agent has i.i.d. values across rounds, then in the worst case, she can never get more than a constant strictly less than $1$ fraction of her ideal utility -- her highest achievable utility given her nominal share of resources. Moreover, an agent can achieve at least half her utility under carefully designed `pseudo-market' mechanisms, even though other agents may act in an arbitrary (possibly adversarial and collusive) manner. We show that this robustness guarantee also holds under the much simpler DMMF mechanism. More significantly, under mild assumptions on the value distribution, we show that DMMF in fact allows each agent to realize a $1 - o(1)$ fraction of her ideal utility, despite arbitrary behavior by other agents. We achieve this by characterizing the utility achieved under a richer space of strategies, wherein an agent can tune how aggressive to be in requesting the item. Our new strategies also allow us to handle settings where an agent's values are correlated across rounds, thereby allowing an adversary to predict and block her future values. We prove that again by tuning one's aggressiveness, an agent can guarantee $\Omega(\gamma)$ fraction of her ideal utility, where $\gamma\in [0, 1]$ is a parameter that quantifies dependence across rounds (with $\gamma = 1$ indicating full independence and lower values indicating more correlation). Finally, we extend our efficiency results to the case of reusable resources, where an agent might need to hold the item over multiple rounds to receive utility.

翻译：我们通过一种动态最大最小公平（DMMF）机制研究多轮次中竞争主体对共享资源的分配问题：每一轮中的商品被分配给迄今为止获得分配次数最少的请求主体。先前研究表明，当主体的价值在轮次间独立同分布时，在最坏情况下其所获效用永远不会超过理想效用——即在其名义资源份额下可实现的最大效用——的严格小于1的常数比例。此外，即使其他主体可能采取任意（可能敌意且合谋）行为，在精心设计的“伪市场”机制下，主体仍能实现至少一半的理想效用。我们证明这一鲁棒性保证在更为简洁的DMMF机制下同样成立。更重要的是，在关于价值分布的温和假设下，我们表明DMMF机制实际上能让每个主体实现 $1 - o(1)$ 比例的理想效用，尽管其他主体可能采取任意行为。我们通过刻画在更丰富策略空间下实现的效用来完成这一证明，其中主体可调整请求商品的激进程度。我们的新策略还能应对主体价值在轮次间存在相关性的场景，从而允许对手预测并阻碍其未来价值。我们证明，通过调整激进程度，主体仍能保证 $\Omega(\gamma)$ 比例的理想效用，其中 $\gamma\in [0, 1]$ 是量化轮次间依赖程度的参数（$\gamma = 1$ 表示完全独立，较低值表示更高相关性）。最后，我们将效率结果扩展至可复用资源场景，即主体需持有商品多轮才能获得效用的情况。