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matching

Author(s): 
IN-KOO CHO AND AKIHIKO MATSUI
Date: 
Fri, 2010-09-17
Abstract: 
This paper provides a decentralized dynamic foundation of the Zeuthen-Nash bargaining solution, which selects an outcome that maximizes the product of the individual gains over the disagreement outcome. We investigate a canonical random matching model for a society in which two agents are drawn from a large population and randomly matched to a partnership, if they successfully find an agreeable payoff vector. In each period, the two agents choose to maintain or terminate the partnership, which is subject to a small exogenous probability of break down. We show that as the discount factor converges to 1, and the probability of exogenous break down vanishes, the Zeuthen-Nash bargaining solution emerges as a unique undominated equilibrium outcome. Each agent in a society, without any centralized information processing institution, behaves as if he has agreed upon the Zeuthen-Nash bargaining solution, whenever he is matched
to another agent. 
 
Author(s): 
Fuhito Kojima
Date: 
Wed, 2009-01-21
Abstract: 
Stability is a central concept in matching theory, while nonbossiness is im-
portant in many allocation problems. We show that these properties are incompatible:
There does not exist a matching mechanism that is both stable and nonbossy.
Author(s): 
Fuhito Kojima
Date: 
Wed, 2009-01-21
Abstract: 
This paper proposes a new stability concept in matching markets
between schools and students, robust stability. A mechanism is ro-
bustly stable if it is stable, strategy-proof and also immune to a com-
bined manipulation, where a student first misreports her preferences
and then blocks the matching that is produced by the mechanism.
First, we show an impossibility result: Even when school priorities
are publicly known and only students can behave strategically, there
is no robustly stable mechanism. Our main result characterizes the
market conditions under which a robustly stable mechanism exists.
Specifically, we show that there exists a robustly stable mechanism if
and only if the priority structure of schools is acyclic (Ergin 2002),
and in that case, the student-optimal stable mechanism is the unique
robustly stable mechanism.