Stable systems of schedule contracts

The paper studies the systems of paired contracts between agents of two complementary groups (workers and firms, students and universities, depositors and banks). Multiple contracts are allowed, as well as flexible contracts when the contract is concluded with some intensity. Agent preferences are described using choice functions. It is shown that if these choice functions satisfy the condition that we call conservativeness, then there are so-called stable systems of contracts, when it is unprofitable for any pair of counterparties to change the concluded contracts. The existence of a stable system of contracts is established using the transfinite process of sequential approximation, which generalizes the classical Gale?Shapley algorithm. As a result, we relieved of the finiteness conditions of the set of contracts. Such properties of stable systems as polarization and latticeness are also studied.