Online Resource Sharing via Dynamic Max-Min Fairness: Efficiency, Robustness and Non-Stationarity

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