||"A Two Stage Model of Assignment and Market"|
Matsui, Akihiko and Megumi Murakami
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This paper studies a two stage economy where the non-monetary assignments of indivisible objects are followed by market transactions. In this economy, there are finitely many players and finitely many types of indivisible objects and one divisible good called money. Every player demands at most one object besides money. The first stage is governed by a non-monetary assignment mechanism, while the second stage is governed by the market. We impose the obtainability condition on the first stage mechanism, which requires that each player has an option to obtain any unassigned object. This condition is satisfied by a broad class of mechanisms, including the Boston mechanism and deferred acceptance algorithm. We define an equilibrium concept called perfect market equilibrium (PME) and its refined concept. We then analyze three classes of situations, the case with abundant money, the case where some players (e.g., firms) cannot obtain objects (e.g., degree) in the first stage, waiting for some other players (e.g., students) obtain them and trade the objects with them in the future, and the third case with no money. We set forth some sufficient conditions under which existence and efficiency are guaranteed and compare the three situations in terms of these conditions.