Mathematical Matchmaking

The main mathematical news

1962: Gale and Shapley presented and algorithm for finding a stable matching for any equal numbers of men and women.

1984: Roth, a professor of economics, applied the Gale-Shapley algorithm to explain market behavior.

2012: The Nobel Prize in Economics was awarded to Shapley and Roth (Gale was no longer alive).

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Additional Theorems / conjectures / Open questions

Stable Roommate Problem – how to find a stable matching for any even-sized set. This is a generalization of SMP, and in some cases no stable matching exists.

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The main mathematical concepts / Principles

Game theory (MSC2010#97K99)

  • Combinatorics
  • Stable Marriage
  • Gale-Shapley algorithm
  • Factorial (n!)

Logic (MSC2010#97E30) 

  • Proof by contradiction
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