Jealousy-freeness and other common properties in Fair Division of Mixed Manna
This work addresses fair allocation problems in economics and AI, providing theoretical insights for scenarios with mixed items, though it appears incremental as it builds on existing fair division concepts.
The paper tackled the problem of fair division of mixed manna, where items can be good, bad, or mixed for agents, by studying axiomatic properties like jealousy-freeness up to one item and Pareto-optimality, obtaining new possibility and impossibility results and advancing computational tasks in this area.
We consider a fair division setting where indivisible items are allocated to agents. Each agent in the setting has strictly negative, zero or strictly positive utility for each item. We, thus, make a distinction between items that are good for some agents and bad for other agents (i.e. mixed), good for everyone (i.e. goods) or bad for everyone (i.e. bads). For this model, we study axiomatic concepts of allocations such as jealousy-freeness up to one item, envy-freeness up to one item and Pareto-optimality. We obtain many new possibility and impossibility results in regard to combinations of these properties. We also investigate new computational tasks related to such combinations. Thus, we advance the state-of-the-art in fair division of mixed manna.