Random path to stability in a decentralized market with contracts

Beatriz Millán () and Eliana Pepa Risma
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Beatriz Millán: Universidad Nacional de San Luis and CONICET

Social Choice and Welfare, 2018, vol. 51, issue 1, No 5, 79-103

Abstract: Abstract For a many-to-many matching model with contracts in which the preferences of all hospitals satisfy substitutability and the preferences of all doctors satisfy substitutability, the 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 a unilateral 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.

Date: 2018
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DOI: 10.1007/s00355-018-1108-6

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