Random Path to Stability in a Decentralized Market with Contracts

BEATRIZ MILLÁN; ELIANA PEPA RISMA

Santiago

Workshop; Workshop on Matching and Market Design; 2016

Milklenium Institute, Universidad de Chile

For a many-to-many matching model with contracts in which the preferences of all hospitals satisfy sustitutability and the preferences of all doctors satisfy substitutability, law of aggregate demand and q-congruence, we show the existence of a convergent blocking path. In other words, we start from an arbitrary allocation and build a finite sequence of allocations leading to a stable outcome, with the special feature that each allocation can be obtained from the previous one by satisfying an one-sided block or a bilateral blocking contract. As a consequence, we prove that the process of allowing randomly selected blocks to be satisfied eventually leads to a stable outcome. This explains the fact that some markets with contracts reach stable assignments by means of decentralized decisions.