In chapter 3 an algorithm called top-trading cycles (TTC) was introduced to us. Briefly, TTC is an algorithm for trading indivisible items without using money. The basic TTC algorithm is illustrated by the housing market situation, nevertheless, TTC can be used in other situations such as kidney exchange and school choice. Also, there are several extension to this algorithm.
Top Trading Cycles is a method that values efficiency over fairness and has an undesirable feature when objects may be assigned to more than one agent as is the case in the school choice problem. Many people have argue that efficiency and fairness are incompatible in the sense that there may not always exist an assignment that is both fair and efficient, therefore, the algorithm must prioritize between these conditions.
I was searching for more information about this topic and found a research paper written by Thayer Morrill. In this paper the author introduce two simple variations of Top Trading Cycles
in order to mitigate some of the undesirable features of this algorithm, for example, when objects may be assigned to more than one agent as is the case in the school choice problem. The first variation is called “Clinch and Trade” which reduces the number of unnecessary trades and depends on the order in which cycles are processed. The second, First Clinch and Trade, is independent of the order in which cycles are processed but allows more unnecessary trades.
Below you will find the research paper I am talking about. Even though it is not easy to read, I encourage you to have a look at it and take a moment to comment if you were interested.