Imagine yourself as a matchmaker with female clients, denoted by the set [A, B, C, D], and male clients, denoted by the set [a, b, c, d]. You are tasked to arrange 4 stable es of the maidens listed in order of preference, and each woman similarly ranks the men. A marriage ( M ) is deemed stable when there are no dissatisfied pairs. For the couples a-D and b-C, if man D prefers woman b (the wife of another man) AND woman b also favors man D to C, both marriages will soon collapse. A duo is only unstable if both D and b choose to forgo their current mates for each other. If man D admires woman b, but she does not reciprocate, no dissatisfied pair is created – unrequited extramarital affection will still result in stable sets .
In the pair a-A, man a is delighted because woman A is his optimal wife. However, woman A may still pursue better options, such as men d or c. If both d and c would be more satisfied with A than their existing partners, A will prioritize d. Yet if man d is uninterested but man c is happy to oblige, c-A will emerge as a new stable pair