Online Resource Sharing via Dynamic Max-Min Fairness: Efficiency, Robustness and Non-Stationarity
CoRR(2023)
摘要
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 Ω(γ) fraction of her ideal
utility, where γ∈ [0, 1] is a parameter that quantifies dependence
across rounds (with γ = 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.
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