In essence, each hospital at each round offers its position to its most preferred applicant. Students offered a place are then tentatively matched with their favourite among the hospitals making them an offer. Their names are then stricken from the submitted rankings of all those hospitals which they ranked lower than the one with which they are tentatively matched, and the process is repeated using the hospitals' revised rankings. This means that students who have moved to the top of some hospital's rankings will now get offers from that hospital. Members can never find a set of matches that involves only members of the group that is better for all of them than the match initially proposed' Regardless of what group of students and hospitals may form to seek alternative matches, the members can never find a set of matches that involves only members of the group that is better for all of them than the match initially proposed by the Matching Program.
Stability is a very demanding condition.
The fact that the Matching Program's matches are stable helps to explain the persistence of the scheme. The book looks at the future of business and economic systems. Firms in Germany obtain about 90 per cent of their financing from banks, who in turn are represented on the firms' supervisory boards. A large fraction of all US stocks, especially those of the larger firms, are held by institutional investors, such as insurance companies, mutual funds, and pension plans. It has often been claimed that institutional investors are especially fickle and impatient and their rise has been blamed for the short-term performance pressures that managers claim to feel.