0. 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
Presentation for: MGT 703: Experimental Economics

1. What’s so special about March 15, 2007?
It’s Match Day!
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
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2. Agenda Matching markets Experimental setup Results from experiment
Discussion
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3. Why is matching important?
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
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
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4. What happens when matching markets fail?
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
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
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
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5. How do we match?
Centralized matching is usually achieved through algorithms
Take into account preferences of both parties
Result in ‘market-clearing’ (to the extent possible…)
In the example from the UK, two algorithms were used
“Newcastle” algorithm – introduced in Newcastle and Birmingham in
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
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6. 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
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7. 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
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8. 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?
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9. Experimental Setup Steps in Experiment Sample Payoff Table
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
Payoffs shown to Firm 1
(a high-productivity firm)
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10. 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
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11. Results (1): Efficacy of centralized matching
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12. : Centralized matching initially reduces pre-emptive matches
Results (2)
: Centralized matching initially reduces pre-emptive matches
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13. Results (3): Mismatch costs modulate levels of unraveling
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14. Discussion Questions/Comments?
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?
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