Efficient Allocation of Free Stuff
adaptive agents and multi-agents systems(2019)
摘要
We study online matching settings with selfish agents when everything is free. Inconsiderate agents break ties arbitrarily amongst equal maximal value available choices, even if the maximal value is equal to zero. Even for the simplest case of zero/one valuations, where agents arrive online in an arbitrary order, and agents are restricted to taking at most one item, the resulting social welfare may be negligible for a deterministic algorithm. This may be surprising when contrasted with the 1/2 approximation of the greedy algorithm, analogous to this setting, except that agents are considerate (i.e., they don't take zero-valued items). We overcome this challenge by introducing a new class of algorithms, which we refer to as prioritization algorithms. We show that upgrading a random subset of the agents to "business class" already improves the approximation to a constant. For more general valuations, we achieve a constant approximation using log n priority classes, when the valuations are known in advance. We extend these results to settings where agents have additive valuations and are restricted to taking up to some q >= 1 items. Our results are tight up to a constant.
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关键词
Online matching,Welfare approximation,Selfish agents
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