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We consider a fair division setting where indivisible items are allocated toagents. Each agent in the setting has strictly negative, zero or strictlypositive utility for each item. We, thus, make a distinction between items thatare good for some agents and bad for other agents (i.e. mixed), good foreveryone (i.e. goods) or bad for everyone (i.e. bads). For this model, we studyaxiomatic concepts of allocations such as jealousy-freeness up to one item,envy-freeness up to one item and Pareto-optimality. We obtain many newpossibility and impossibility results in regard to combinations of theseproperties. We also investigate new computational tasks related to suchcombinations. Thus, we advance the state-of-the-art in fair division of mixedmanna.

Jealousy-freeness and other common properties in Fair Division of Mixed Manna