As we’ve seen on class, the top trading cycle mechanism finds allocations over preferences which are strategic proof and individually rational. In this topic I’ll like to propose an alternative model which induces the same outcome as TTC, and it’s also strategic proof and individually rational. This mechanism is a house allocation problem called “you get my house, I get your turn” (YRMH-IGYT), where not every individual has an initial endowment. The idea of the mechanisms is to follow the random ordering in descending order, highest ranked individual will point at his/her top choice and leave his/her initial endowment available; the chosen house will point to its owner; then the owner moves to the top of the ordering and will point to his/her top choice available. The mechanisms will continue until an individual points at an available house then an exchange will take place and individuals and houses assigned on step one will leave the market; that will be the end of step one. From step two all the way to step N will follow as before but only with remaining individuals and houses, the mechanisms will stop once every individual is assigned to a house. Note: whenever there is a vacant house, for both mechanisms, it points to the highest ranked individual.
To illustrate the mechanism I will solve a basic example with both a TTC and YRMH-IGYT, and show that both mechanisms lead to the same allocation.
As shown on the exercise solution, both mechanisms lead to the same allocation outcome under this random ordering.