A Two Stage Model of Assignment and Market

27 Pages Posted: 21 Aug 2017 Last revised: 4 Jan 2018

See all articles by Akihiko Matsui

Akihiko Matsui

University of Tokyo - Faculty of Economics

Megumi Murakami

Northwestern University, Department of Economics, Students

Date Written: January 4, 2018


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. As a mechanism in the first stage, this paper considers the Boston mechanism and the deferred acceptance algorithm. This paper defines perfect market equilibrium (PME) where the second stage outcome is a market equilibrium both on and off the equilibrium paths, and the first stage strategy profile is a Nash equilibrium of the mechanism, taking the second stage outcomes as given. This paper then analyzes two situations, the economies with and without money. We also applied our analysis to the college admission problem: some players (firms) cannot obtain objects (degrees) in the first stage, waiting for some other players (students) obtaining them, and buy the objects (hire the students with degrees) through the market in the second stage. This paper provides us with some necessary and sufficient conditions under which efficiency and stability are guaranteed.

Keywords: Two Stage Economy, Assignment Mechanism, Market, Indivisible Object, Perfect Market Equilibrium, Scarcity, Priority Cycle, Stability

JEL Classification: C78, D41, D47, D51

Suggested Citation

Matsui, Akihiko and Murakami, Megumi, A Two Stage Model of Assignment and Market (January 4, 2018). Available at SSRN: https://ssrn.com/abstract=3020547 or http://dx.doi.org/10.2139/ssrn.3020547

Akihiko Matsui

University of Tokyo - Faculty of Economics ( email )

7-3-1 Hongo, Bunkyo-ku
Tokyo 113-0033

Megumi Murakami (Contact Author)

Northwestern University, Department of Economics, Students ( email )

Evanston, IL
United States

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