In chapter 3 we read about top-trading cycles (TTC), which helps given indivisible trading items without the necessity of using money.
In the paper from Thayer Morrill “An alternative characterization of top trading cycles”, he provides a different explanation to what differentiates top trading cycles from all other strategy proof and efficient mechanisms.
It is interesting to notice that TTC loses some of its desirable properties when objects may be assigned to more than one agent.
Even though in the chapter it is mentioned that there is a chance for it to not work in an exchange economy, since it may be hard to identify Pareto inefficiency. Then, what when objects may be assigned to at most one agent?
Given this, we should take a look at strategy proofness and weak maskin monotonicity.
Top Trading Cycles is the only such mechanism that satisfies mutual best and independence of irrelevant rankings. Both of there properties are desirable attributes of an allocation mechanism.