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

Most Competitive Mechanisms in Online Fair Division