The solution to this problem can be "oriented" to one group or the other, which implies that each agent in the suboptimal group has the worst possible outcome out of all possible solutions to this problem. When solving this problem, once a passive agent is no longer free, it can never again be free. The original algorithm to solve this problem runs iterative rounds whereby one set of agents can trade up while agents in the other set are tasked with making offers to the best available candidate; that algorithm by (*) Gale and Shapley first prove
The solution to this problem can be "oriented" to one group or the other, which implies that each agent in the suboptimal group has the worst possible outcome out of all possible solutions to this problem. When solving this problem, once a passive agent is no longer free, it can never again be free. The original algorithm to solve this problem runs iterative rounds whereby one set of agents can trade up while agents in the other set are tasked with making offers to the best available candidate; that algorithm by (*) Gale and Shapley first proved that this problem is always solvable. Each agent ranks its preferences before a solution tries to eliminate blocking pairs in which two agents prefer to be paired with each other rather than their current partners. For 10 points, name this problem of finding a pairing of men and women such that no pairs want to switch partners.
The solution to this problem can be "oriented" to one group or the other, which implies that each agent in the suboptimal group has the worst possible outcome out of all possible solutions to this problem.
stable marriage problem [or stable matching problem; prompt on partial answers]