Fair Allocation with Special Externalities

Most of the existing algorithms for fair division do not consider externalities. Under externalities, utility an agent depends only on its allocation but also other agents’ allocation. An has a positive (negative) value assigned goods (chores). This work studies special case externality which we refer to as 2-D. In 2-D, receives or negative unassigned items independent who them. We propose simple valuation transformation and show that can adapt using it retain some fairness efficiency notions in However, proportionality doesn’t extend redefine PROP relaxation algorithms. Further, prove maximin share (MMS) may have any multiplicative approximation this setting. Studying domain is stepping stone towards full externalities where ensuring much more challenging.