On the Existence of Stable Allocations in Matching Games with Infinite Contracts : Leveraging the Deferred Acceptance Algorithm

In classic matching games, individuals choose their partners and each pair chooses a contract from a finite set of feasible contracts; the existence of stable allocations then follows from the (generalized) Deferred Acceptance algorithm. We consider an extension where the contract set is a compact subset of a Banach space (e.g., R^k or C[0, 1]) and establish, using only elementary methods, that this algorithm continues to ensure the existence of stable allocations