Among Shapley’s incredible contributions to theoretical economics, the matching algorithm he developed with David Gale in 1962 would appear relatively insignificant. He developed the Shapley value (a “fair” way of dividing surplus in cooperative games), he characterised the core (a set of outcomes that cannot be improved on by a group of players) in a large class of (“convex”) games, and, more recently developed “potential games”, which find applications in many areas, including engineering.
But thanks to Al Roth (and others, including Vince Crawford), it is precisely Shapley’s algorithm that changed the way we think about markets. What “market designers” realised is that a stability and truth-telling in a market can be just as important efficiency (and that it’s not possible to achieve all three!) in applications. Roth’s work turned Shapley’s marriage market from an intellectual curiosity to a cornerstone of economic theory and practice. He also made it cool.