Título: "Random Path to Stability in a Model of Matching with Contracts".
Expositor: Beatriz Millan y Eliana Pepa
Abstract: For a model of many-to-many matching with contracts where all hospitals have substitutable preferences and all doctors have q-responsive preferences, we show the existence of a convergent path of stabilization; that is to say, we start from an arbitrary allocation and build a finite sequence of allocations leading to a stable outcome, with the particularity that each allocation in that succession can be obtained from the previous one by satisfying an one-side blocking or a bilateral blocking contract. As a consequence, we prove that the process of allowing randomly selected blocking contracts to be satisfied converges to a stable outcome with probability one. This explains the fact that some markets reach stable assignments by means of decentralized decisions.