Before revision:  To the best of our knowledge, we are the first to address the problem of finding a leximin optimally fair and stable matching .
After revision:  To the best of our knowledge, we are the first to address the problem of finding a leximin optimal stable matching is NP-Hard, even under isometric utilities. In fact, when additivity is the only assumption on the utilities, we show that, unless P=NP, no polynomial time approximation is possible .