I was wondering how you would call a market for kidney donors and recipients, where you have many 'buyers' and many 'sellers'. However, the 'seller' can only 'sell' his/her 'product' once. Since it's illegal to sell kidneys, the market structure is a little bit vague for me to categorize. Suppose selling and buying kidneys would be legal, how would that market be called?
Generally, these types of markets are called matching markets. That's also the same term given to a variety of economic decisions and market structures, from school choice to some types of marriage problems.