Math

Stable matching

Watch Gale–Shapley matching progress through proposals, tentative engagements and rejections. Reverse the proposing side and verify the absence of blocking pairs at completion.

By Mykhailo Makarov

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Step through Gale–Shapley proposals and rejections. Each side has strict random preferences. Reverse the proposing side to compare outcomes; a completed matching has no blocking pair.

Equations used in the module

Equations
A free proposer asks the highest-ranked untried receiver
A receiver keeps the preferred offer and rejects the other
At most n² proposals; complete strict lists yield a stable matching
Proposer-optimal among stable matchings

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