A group of friends organize their tennis games by submitting each their availability over the weekdays. They want to obtain an assignment such that: each game must be a double tennis match, i.e. requires four people, and nobody plays in a day he is unavailable. Can we construct assignments that will always produce efficient, fair, and envy-free outcomes? The answer is no, and extends to any sport that requires any group size.
Cite
@article{arxiv.1608.08085,
title = {Playing Tennis without Envy},
author = {Josue Ortega},
journal= {arXiv preprint arXiv:1608.08085},
year = {2016}
}