September 25, 2007

Reorganization in Matching Markets

The Dynamics of Reorganization in Matching Markets: A Laboratory Experiment Motivated by A Natural Experiment- John H Kagel and Alvin E Roth

September 25, 2007

Presentation for: MGT 703: Experimental Economics

Yale School of Management 20070925_Matching_Games.ppt 2

It’s Match Day!

What’s so special about March 15, 2007?

The National Residency Matching Program matches residents and independent applications to residencies all over the country

In 2006, the program matched– 16,000 medical school students– 18,000 independent applicants– 24,085 positions

Efficient matching is what keeps thousands of medical residents across the country happy!

This is what matching markets are about


Matching markets

Experimental setup

Results from experiment

Discussion

Agenda


Why is matching important?

Unstable matches can occur because– Types are not known (signaling, pre-emption, etc.)– Known congestion in the system

But matching efficiently is not easy– Decentralized matching may be acceptable in some cases– Other situations call for centralized mechanisms

Matching markets are centralized clearinghouses– They attempt to match up as ‘fairly’ as

possible

Efficient matching markets allow parties to match with their best possible counterpart– The “fit” factor in job interviews– A stable match is beneficial to both parties


What happens when matching markets fail?

An example: In mid-1960s regional market for new physicians in UK unraveled– Medical students were being made offers a year and a half prior o

graduation

Matching markets can unravel– Individual agents attempt to pre-empt the matching market– This can have significant costs

- Mismatches based on insufficient data- Lost opportunities

Another example: Market for Federal court clerks (US) – Becker, Beyer and Calabresi (1994) call for reorganization of

matching market due to earlier unraveling– This attempt was also unsuccessful


How do we match?

In the example from the UK, two algorithms were used– “Newcastle” algorithm – introduced in Newcastle and Birmingham in 1966-67

- Resulted in unstable match-ups- Unraveled: by 1981, 80% of preferences submitted by both students and positions indicated only a mutual first choice - This is “match-fixing” in its truest form!

– Delayed Acceptance (DA) algorithm – introduced in Edinburgh in 1969 and Cardiff in 1971- Based on Gale-Shapley (1962) result- Resulted in stable match-ups

Centralized matching is usually achieved through algorithms– Take into account preferences of both parties– Result in ‘market-clearing’ (to the extent possible…)


The Newcastle Algorithm

Step 1: Firms and workers submit their preferences

Step 2: Each firm-worker combination is ranked (ascending order)– Based on product of firm ranking of worker multiplied by worker’s ranking of firm

Step 3: If necessary, ties are broken based on local rules– i.e. more weight can be given to the worker’s preference or the firm’s preference

Step 4: Matches are identified from the ranked list


Delayed Acceptance Algorithm

Step 1:

Each employer makes an offer to its highest ranked acceptable student

Step k:

(i) Each worker rejects all but the highest-ranked of the acceptable offers she received in steps 1 through k – 1

(ii) Each employer who has had an offer rejected in part (i) of step k, makes an offer to its highest ranked acceptable worker who has not yet rejected its offer

(iii) The algorithm stops at any step k = T at which no rejections are issued, and the resulting matching places each worker with the employer (if any) whose offer she has not rejected


Motivation of the Experiment

Authors have seen a “natural experiment” in introduction of centralized market clearinghouses (UK, late 1960s)

In this experiment, regions introduced centralized matching algorithms to halt unraveling– Inconsistent success; some regions succeeded in slowing unraveling; others did not– Initial “pull-back” in pre-emptive decentralized matching– Longer term effects depend on algorithm efficacy

Can we replicate such an experiment in the lab?

What will it tell us about transitions to centralized matching markets?


Experimental Setup

Steps in Experiment

Six firms are asked to match with six workers

– Three “high” type and three “low” type of each

–Known payoff tables

Three time periods: -2, -1 and 0

One-offer per period rule except when centralized matching occurs

Offering/accepting early has costs

First 10 rounds are all decentralized matching

Subsequent 15 rounds have centralized matching in period 0

Sample Payoff Table

Payoffs shown to Firm 1 (a high-productivity firm)


Sample Payoff Matrix

Comments

Setup is designed to cause congestion

Making any match is better than making no match

Big upside for correct matches for “high” types


Results (1): Efficacy of centralized matching


: Centralized matching initially reduces pre-emptive matchesResults (2)


Results (3): Mismatch costs modulate levels of unraveling


Discussion

Simple experiment that maps closely to what was observed in reality

Creation of an in-lab model of regime changes– Provides a lot of insight over and above a static model– Authors also explore modulating factors

In our preliminary in-class test, I hope to see some unraveling occurring

Questions/Comments?

Documents

September 25, 2007