Question

Four men (Adam, Alan, Aldo, Alex) are to be paired with four women (Bala, Barb, Beth, Bree) using the Gale-Shapley Algorithm. Their prefer- ences are shown here: 1st 2nd 3rd 4th AdamBarb Beth Bree Bala Alan Bala Beth Barb Bree Aldo Bala Bree Barb Beth AlexBeth Barb Bala Bree 4th 2nd 3rd 1st ex Barb Alan AlexAdam Aldo Beth Aldo Adam Alex Alan Bree Adam Alan Aldo Alex Using the women as the proposers, deter stable perfect matching of these eight people mine a Using the same eight people and preferences listed above, determine a stable perfect matching of these eight people if men are the proposers. But wait DNA testing has just revealed that Alan and Barb are long-lost brother and sister, so they cannot be married. If the men are the pro- posers, does a stable perfect matching exist with this added restriction?

Answer 1

An Swes! The (niven info mation end male Adlam Aldo 4 2nd Fe st Barb → Alan Leth - Adam dam shou Prefemence is Adsm. so he shoul not He should fo fon Bath

neth'sfinst pnefenence is Aldo unth eference ,'s Beth 2) flan inst pre fenerde İs Asia Rala's ind Pnefenece i Hen Alan shou lá go fom Bet bul ounb Prefeneme is Han Peteenseis Alan He should fBanb Aldo should go fo fala G, Lnee