Reallocation with priorities

Abstract

We consider a reallocation problem with priorities where each agent is initially endowed with a house and is willing to exchange it but each house has a priority ordering over the agents of the market. In this setting, it is well known that there is no individually rational and stable mechanism. As a result, the literature has introduced a modified stability notion called μ0-stability. In contrast to college admission problems, in which priorities are present but there is no initial endowment, we show that the ownership-adjusted Deferred Acceptance mechanism identified in the literature is not the only individually rational, strategy-proof and μ0-stable mechanism. By introducing a new axiom called the independence of irrelevant agents and using the standard axiom of unanimity, we show that the ownership-adjusted Deferred Acceptance mechanism is the unique mechanism that is individually rational, strategy-proof, μ0-stable, unanimous and independent of irrelevant agents.