This paper combines two key ingredients for online algorithms - competitive analysis (e.g. the competitive ratio) and advice complexity (e.g. the number of advice bits needed to improve online decisions) - in the context of a simple online fair division model where items arrive one by one and are allocated to agents via some mechanism. We consider four such online mechanisms: the popular Ranking matching mechanism adapted from online bipartite matching and the Like, Balanced Like and Maximum Like allocation mechanisms firstly introduced for online fair division problems. Our first contribution is that we perform a competitive analysis of these mechanisms with respect to the expected size of the matching, the utilitarian welfare, and the egalitarian welfare. We also suppose that an oracle can give a number of advice bits to the mechanisms. Our second contribution is to give several impossibility results; e.g. no mechanism can achieve the egalitarian outcome of the optimal offline mechanism supposing they receive partial advice from the oracle. Our third contribution is that we quantify the competitive performance of these four mechanisms w.r.t. the number of oracle requests they can make. We thus present a most-competitive mechanism for each objective.

中文翻译：

---

线上展会分工最具竞争力的机制

本文结合了在线算法的两个关键要素——竞争分析（例如竞争比率）和建议复杂性（例如，改进在线决策所需的建议位数）——在一个简单的在线公平划分模型的背景下，项目一个接一个到达一个并通过某种机制分配给代理。我们考虑四种这样的在线机制：流行的 Ranking 匹配机制，改编自在线二分匹配等，平衡的 Like 和 Maximum Like 分配机制首次引入在线公平划分问题。我们的第一个贡献是我们根据匹配的预期规模、功利主义福利和平等主义福利对这些机制进行了竞争分析。我们还假设预言机可以为这些机制提供许多建议位。我们的第二个贡献是给出了几个不可能的结果；例如，假设它们从预言机接收部分建议，则没有任何机制可以实现最佳离线机制的平等结果。我们的第三个贡献是我们量化了这四种机制的竞争性能，以及它们可以发出的预言机请求的数量。因此，我们为每个目标提出了一个最具竞争力的机制。