Gale Shapley

The Gale-Shapley algorithm, developed by David Gale and Lloyd Shapley in 1962, addresses the problem of matching preferences, often illustrated through marriage or job assignments. In this process, participants rank their preferences (like individuals ranking potential partners). The algorithm ensures stable matches, meaning no pair would prefer each other over their assigned partner. It operates by allowing participants to propose and be rejected iteratively until a stable, mutually agreeable outcome is reached. Its concepts are widely applicable, influencing fields like economics, computer science, and market design, where stable relationships or allocations are desired.