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

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 Yale School of Management

Agenda Matching markets Experimental setup Results from experiment Discussion Yale School of Management

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 Yale School of Management

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 Yale School of Management

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 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 Yale School of Management

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 Yale School of Management

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 Yale School of Management

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? Yale School of Management

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) Yale School of Management

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 Yale School of Management

Results (1): Efficacy of centralized matching Yale School of Management

: Centralized matching initially reduces pre-emptive matches Results (2) : Centralized matching initially reduces pre-emptive matches Yale School of Management

Results (3): Mismatch costs modulate levels of unraveling Yale School of Management

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? Yale School of Management