A Two-Stage Model of Assignment and Market

29 Pages Posted: 21 Aug 2017 Last revised: 25 Jan 2019

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 24, 2019

Abstract

Centralized matching mechanisms and decentralized markets have been widely studied to allocate indivisible objects. However, they have been analyzed separately. The present paper proposes a new framework, by explicitly formulating a two-stage model where objects are allocated through a matching mechanism in the first stage and traded in the second stage market. In addition, one divisible good called money may or may not be available in the market. Every player demands at most one unit of object besides money. The players may face different priorities at each object type in the first stage. Each object type has a limited amount of capacity, called quota. Each player has a quasi-linear utility function.
The present analysis sets forth the equivalence conditions under which stability and efficiency are attained in equilibrium.

Keywords: two-stage economy, deferred acceptance algorithm (DA), market, indivisible object, perfect market equilibrium (PME), priority, stability, cyclical priority, unreversed priority, minimal demand

JEL Classification: C78, D41, D47, D51

Suggested Citation

Matsui, Akihiko and Murakami, Megumi, A Two-Stage Model of Assignment and Market (January 24, 2019). 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
Japan

Megumi Murakami (Contact Author)

Northwestern University, Department of Economics, Students ( email )

Evanston, IL
United States

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