Abstract
We study deferred acceptance algorithm (DA) with retrade by formulating a two-stage model where DA is played in the first stage, and a decentralized market opens in the second. Both non-monetary and monetary retrades are considered. Perfect market equilibrium (PME) is defined: market equilibrium prevails in the second stage both on and off the path, and Nash equilibrium is played in the first stage game induced by the second-stage markets.In the economies with no money, the stable and Pareto optimal allocation is the truthful PME allocation if and only if the priority structure is acyclical. A pure PME object allocation is unique if and only if the priority structure is unreversed. In the economies with money, an efficient PME allocation exists if and only if the minimum demand across tangible objects exceeds a certain threshold. A pure PME object allocation is always unique.
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