Consider the following one-sided matching market. That is, anyone can match with anyone (this is often...

 

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Consider the following one-sided matching market. That is, anyone can match with anyone (this is often referred to as the "roommate" problem). There are four people, Ann, Barry, Clara, and Dan. They must pair off as each will share a two-bed room. Each has preferences over which of the others they would like to have as a room mate. In decreasing order of preference, the preferences for everybody are given as follows: Ann: Barry, Clara, Dan Barry: Clara, Ann, Dan Clara: Ann, Barry, Dan Dan: Clara, Ann, Barry Show that no stable matching exists in this one-sided matching market. Consider the following one-sided matching market. That is, anyone can match with anyone (this is often referred to as the "roommate" problem). There are four people, Ann, Barry, Clara, and Dan. They must pair off as each will share a two-bed room. Each has preferences over which of the others they would like to have as a room mate. In decreasing order of preference, the preferences for everybody are given as follows: Ann: Barry, Clara, Dan Barry: Clara, Ann, Dan Clara: Ann, Barry, Dan Dan: Clara, Ann, Barry Show that no stable matching exists in this one-sided matching market.

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To determine if a stable matching exists we need to consider whether there is a situation where no p... View the full answer