Top trading cycle (TTC) is an algorithm for trading indivisible items without using money.
TTC is a truthful mechanism. This was proved by Alvin Roth.[3] When the preferences are strict (there are no indifferences), TTC always finds a strictly Pareto-efficient allocation. Moreover, it always finds a core-stable allocation. Moreover, with strict preferences, there is a unique Core-Stable allocation, and it is the one found by TTC.
In the strict preferences domain, TTC is the only mechanism that satisfies Individual rationality, Pareto efficiency and Strategy-proofness.
https://en.m.wikipedia.org/wiki/Top_trading_cycle
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