Market
NRMP-like market
The defaults: 1,000 applicants in NRMP-like groups for 926 positions in 142 programs (1.08 applicants per position), moderate agreement on both sides, and noisy views before interviews.
Idealized market
One measure on each side, seen exactly: applicants rank programs by quality alone and programs rank applicants by strength alone, with no taste and no noise at any stage. Applications and interviews keep the NRMP-like limits, so the match sorts the strongest applicants into the best programs as far as they allow.
Idealized market with signals
The idealized market with signals: each applicant sends 3 gold and 5 silver signals to programs at their own level, and programs pass over stronger applicants who did not signal them. Signals tell programs who would really come, so most of the idealized market's empty positions fill.
Idealized market, signals first
The same signals, but programs invite everyone who signalled them before anyone else. Positions fill, but weaker applicants who signalled take interviews from stronger ones who did not, so the strongest applicants usually match less often.
Noisy market
The idealized market seen through heavy noise: every view of quality and strength is off by a random error three times their spread, too high or too low, interviews correct none of it, and applicants misjudge where they stand. Only the noise differs from the idealized market.
Noisy applicants, perfect programs
The idealized market, but programs cannot judge applicants: every program sees each applicant's strength through a random error three times its spread, before and after interviews. Applicants see every program's quality exactly and know where they stand. Strength stops paying off: the strongest applicants, who apply only to the most sought-after programs, usually match less often than the weakest.
Noisy programs, perfect applicants
The idealized market, but applicants cannot judge programs: every applicant sees each program's quality through a random error three times its spread, before and after interviews. Programs see every applicant's strength exactly, and applicants know where they stand. Who matches follows strength; where they match, much less so.
Small classroom market
60 applicants and 8 programs: quick to run, and small enough to follow every applicant and program.
Preference signals
Each applicant sends 3 gold and 5 silver signals to programs they apply to; 90% of programs read them when choosing whom to interview.
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