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We consider fair division problems where indivisible items arrive one-by-onein an online fashion and are allocated immediately to agents who have additiveutilities over these items. Many existing offline mechanisms do not work inthis online setting. In addition, many existing axiomatic results often do nottransfer from the offline to the online setting. For this reason, we proposehere three new online mechanisms, as well as consider the axiomatic propertiesof three previously proposed online mechanisms. In this paper, we use thesemechanisms and characterize classes of online mechanisms that arestrategy-proof, and return envy-free and Pareto efficient allocations, as wellas combinations of these properties. Finally, we identify an importantimpossibility result.

Strategy-proofness, Envy-freeness and Pareto efficiency in Online Fair Division with Additive Utilities