From Gale-Shapley to the Three-Sided Wall

The Prompt

Explain the achievement of Gale and Shapley's 1962 theorem, the practical success of stable matching in the NRMP and school choice (Roth's work), and then explain why the extension to three-sided matching fails — why stable matchings need not exist and why the decision problem is NP-complete. Cite Gale and Shapley, Roth, and at least one paper on three-dimensional instability.

Completion Criteria

A short essay of three or four paragraphs with at least three citations, clearly marking the boundary between what works and what does not.

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