5 research outputs found
On the Efficiency of the Walrasian Mechanism
Central results in economics guarantee the existence of efficient equilibria
for various classes of markets. An underlying assumption in early work is that
agents are price-takers, i.e., agents honestly report their true demand in
response to prices. A line of research in economics, initiated by Hurwicz
(1972), is devoted to understanding how such markets perform when agents are
strategic about their demands. This is captured by the \emph{Walrasian
Mechanism} that proceeds by collecting reported demands, finding clearing
prices in the \emph{reported} market via an ascending price t\^{a}tonnement
procedure, and returns the resulting allocation. Similar mechanisms are used,
for example, in the daily opening of the New York Stock Exchange and the call
market for copper and gold in London.
In practice, it is commonly observed that agents in such markets reduce their
demand leading to behaviors resembling bargaining and to inefficient outcomes.
We ask how inefficient the equilibria can be. Our main result is that the
welfare of every pure Nash equilibrium of the Walrasian mechanism is at least
one quarter of the optimal welfare, when players have gross substitute
valuations and do not overbid. Previous analysis of the Walrasian mechanism
have resorted to large market assumptions to show convergence to efficiency in
the limit. Our result shows that approximate efficiency is guaranteed
regardless of the size of the market
Competitive Equilibrium from Equal Incomes for Two-Sided Matching
Competitive Equilibrium from Equal Incomes for Two-Sided Matching
Using the assignment of students to schools as our leading example, we study many-to-one
two-sided matching markets without transfers. Students are endowed with cardinal preferences
and schools with ordinal ones, while preferences of both sides need not be strict. Using the
idea of a competitive equilibrium from equal incomes (CEEI, Hylland and Zeckhauser (1979)),
we propose a new mechanism, the Generalized CEEI, in which students face different prices
depending on how schools rank them. It always produces fair (justified-envy-free) and ex ante
e¢ cient random assignments and stable deterministic assignments if both students and schools
are truth-telling. We show that each student's incentive to misreport vanishes when the market
becomes large, given all others are truthful. The mechanism is particularly relevant to school
choice as schools' priority orderings over students are usually known and can be considered
as their ordinal preferences. More importantly, in settings like school choice where agents have
similar ordinal preferences, the mechanismis explicit use of cardinal preferences may significantly
improve eficiency. We also discuss its application in school choice with group-specific quotas
and in one-sided matching
School Admissions Reform in Chicago and England: Comparing Mechanisms by their Vulnerability to Manipulation
In Fall 2009, officials from Chicago Public Schools abandoned their assignment mechanism
for coveted spots at selective college preparatory high schools midstream. After
asking about 14,000 applicants to submit their preferences for schools under one mechanism,
the district asked them re-submit preferences under a new mechanism. Officials
were concerned that \high-scoring kids were being rejected simply because of the order
in which they listed their college prep preferences" under the abandoned mechanism.
What is somewhat puzzling is that the new mechanism is also manipulable. This paper
introduces a method to compare mechanisms based on their vulnerability to manipulation.
Under our notion, the old mechanism is more manipulable than the new Chicago
mechanism. Indeed, the old Chicago mechanism is at least as manipulable as any other
plausible mechanism. A number of similar transitions between mechanisms took place
in England after the widely popular Boston mechanism was ruled illegal in 2007. Our
approach provides support for these and other recent policy changes involving allocation
mechanisms.National Science Foundation (U.S.