Today in class we were reminded that stability implies Pareto efficiency in a matching setup (particularly in the marriage problem). However, while I was reading chapter 3, I noticed that it doesn´t mention if the implication goes both ways (i.e. if Pareto efficiency implies stabilty as well). From previous Microeconomics courses, I remembered that the answer is negative: Pareto efficiency doesn´t imply stability. In this post, I attached a document where I prove this. The method used was a counterexample (since that is sufficient to prove a non-implication). I hope this is useful to you all.
José Pablo López