Top Trading Cycles, explained.
Top trading cycles allocates initially owned indivisible goods by repeatedly executing cycles in which each participant points to the owner of their favourite remaining good.
Why it happens
Three people own houses A, B and C. Strict preference profiles produce either a three-way cycle or self-cycles. Each execution finalises a cycle and removes its participants and houses.
Top trading cycles allocates initially owned indivisible goods by repeatedly executing cycles in which each participant points to the owner of their favourite remaining good.
Read the result
Finalised cycles remove both their participants and owned houses. Remaining preference comparisons concern only what is still available.
A worked example
Trade around a three-person cycle
Inspect A preferring B’s house, B preferring C’s and C preferring A’s.
Execute the cycle to assign each person their favourite house without money.
Reset to the own-house-first profile and execute self-cycles, comparing a different strict preference configuration.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Three people own houses A, B and C. Strict preference profiles produce either a three-way cycle or self-cycles. Each execution finalises a cycle and removes its participants and houses.
Where this idea is useful
A practical use
Recognise how a multiway exchange can make mutually useful trades possible when bilateral swaps are insufficient.
A common misconception
“Every useful exchange must be possible as a bilateral swap.”
A cycle involving several owners can implement trades that cannot be described as a single mutually desirable two-person exchange.
What this explanation leaves out
- One house per person and strict preferences are assumed. Prices, uncertainty, property rights and real exchange constraints are not simulated.
Are the houses reassigned by comparing prices?
No. This housing-market model uses strict ordinal preferences and initial ownership rather than money or market-price estimates.
Could a longer exchange cycle make compatible preferences easier to satisfy?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.