Can Game Theory Explain Dating? Exploring the Stable Matching Algorithm

Stable Matching and Romance

After a game‑theory class the author asks: what kinds of games exist in dating, and how should each side decide to achieve a mutually optimal outcome?

Stable Matching (Gale‑Shapley)

The classic stable matching problem, introduced by David Gale and Lloyd Shapley (Nobel 2012), finds a stable one‑to‑one pairing between two equally sized sets based on preference lists.

Assumed World 999

Consider a parallel world with n men and n women. Each man ranks all women, each woman ranks all men. The following pursuit rules are applied:

Only men propose; a woman can accept (“be my boyfriend”) or reject (“go away”).

A man may propose only while single; each woman can have at most one boyfriend.

A man proposes to the highest‑ranked woman on his list who has not yet rejected him; if a woman already has a boyfriend she keeps the one she prefers more and drops the other.

Men continue proposing until they are matched.

When everyone has a partner, the couples “marry”.

Examples

One man, one woman: No ranking needed; they simply pair.

Two men (A, B) and two women (A, B): Various preference configurations are examined, showing how the proposing side secures its top‑ranked choice while the other side may end up with a less‑preferred partner.

When men propose, the resulting stable matching gives each man his highest possible partner, but some women receive their least‑preferred match. Reversing the roles (women propose) yields the opposite outcome.

Generalization to N

With N men and N women the same reasoning holds: the proposing side is guaranteed to obtain the best possible partner according to its preferences, while the receiving side may be forced into a less‑preferred match.

Conclusion

The analysis shows that in this algorithmic “courtship” the active side has a systematic advantage. Therefore, the practical advice derived is: when a woman likes a man, she should take the initiative.