Simple Proofs of Important Results in Market Design
summary
Sketches of concrete claims and constructive tools: deferred acceptance (DA) is proved verbally to always terminate and yield a man‑optimal stable matching, with three alternate constructions (standard DA, iterative blocking‑pair repair, and a Pareto‑optimal simple‑matching argument). Results extend to many‑to‑one college admissions, give the rural hospital theorem, and generalize to matches with contracts under substitutable preferences. Top trading cycles (TTC) is shown to produce a core allocation and to be strategy‑proof by reducing to a menu/serial‑dictatorship viewpoint.
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