Agent-Based Models of Admissions: Research Foundations

cas_abm_research_foundations.md · 1,794 words · 7 min read

Agent-Based Models of Admissions: Research Foundations

A reader's guide to the matching-markets and ABM literature that grounds college-monte-carlo's two-sided simulation.

College admissions is a two-sided sequential matching market with private information on both sides, holistic review, decentralized round structure, and feedback loops between yield expectations and admit decisions. Closed-form economic models — even sophisticated ones — capture only slices of this. Agent-based simulation captures the full mechanism, but at a methodological cost: ABMs are easy to write and hard to validate. This page is the entry point to the academic literature that informs how college-monte-carlo handles that tradeoff, and to the local mirror of 36 papers + 6 simplified reproductions we keep alongside the simulator's source.

If you came here looking for a single answer to "what is the right model of college admissions," there isn't one. There are five threads of literature that each get something different right, and the pages linked below explain what each one teaches and where college-monte-carlo follows or diverges.

Why ABMs for college admissions

The textbook frame for college admissions is the two-sided matching problem introduced by Gale and Shapley in 1962. In its purest form (deferred acceptance, complete preferences, strict orderings), the problem has clean theorems: a stable matching always exists, can be found algorithmically, and is strategy-proof for the proposing side. School-choice mechanism design is built on top of this foundation, and it has produced real-world successes — most notably the National Resident Matching Program (NRMP) for medical residents.

US college admissions departs from the clean model in at least six ways: it is decentralized (no clearinghouse), runs across multiple rounds with binding commitments (Early Decision functions as a one-sided exploding offer), uses holistic review (subjective, sometimes intransitive preferences), faces capacity uncertainty (yield management — colleges admit more than their seats), bundles financial aid into the match as a contract dimension, and operates under information asymmetries that are themselves correlated with socioeconomic status. The matching-theory primer at College Admissions as a Matching Market walks through each of these in detail.

Once a model has to capture all six of those features simultaneously, closed-form analysis runs out of room. ABMs become the natural toolkit: heterogeneous agents, explicit round structure, calibrated to empirical targets (Common Data Set acceptance rates, yield rates, SAT/GPA distributions, demographic mix), and run as a Monte Carlo over a stochastic logit admission process. The cost is rigor: with enough free parameters an ABM can match any pattern. The discipline that prevents this — calibration against external targets, mechanism decomposition, ablation studies, model selection between rival behavioral specifications — is exactly what the literature below provides.

The literature in one table

The 36-paper corpus mirrored under /research2/cas-abm-references/ is grouped into four tiers by directness of fit to college-monte-carlo's primitives. Tier 1 contains the four matching-markets and school-choice ABMs whose architectural decisions overlap most with our own, plus two methodological references from adjacent domains (kidney exchange, ride-hailing) that we borrow techniques from rather than models.

The full annotated index of all 36 papers — with abstracts, relevance notes, and a four-tier ranking — is kept alongside the simulator's source as research2/CAS-ABM-RELEVANT-PAPERS.md. A dimension-by-dimension comparison of college-monte-carlo against the six papers above (architecture, agent attributes, decision rules, calibration, sequencing, and what each model does that we don't) lives in research2/MATCHING-MARKETS-COMPARISON.md. Both are companion documents to this page rather than rendered web pages.

Tier 1: matching markets and school choice

These are the four papers whose models could in principle have been written about US college admissions. Reading them together is the closest thing to a literature review of "ABMs of college admissions" that exists.

Reardon et al. (2016): Agent-Based Simulation Models of the College Sorting Process

The closest analog to college-monte-carlo. A two-sided ABM of US 4-year college sorting (~1,500 colleges, ELS:2002 + IPEDS calibration, three rounds), whose central methodological move is decomposing the SES-college-quality link into five mechanisms — achievement gaps, application enhancement, information quality, portfolio size, idiosyncratic valuation — and reading off how the SES-by-tier gradient shifts when each is turned off. We have all five mechanisms wired into the simulator; we don't yet have the on/off diagnostic. That diagnostic is the first of three Tier-1 narrative-output extensions on the roadmap.

Dignum et al. (2025): Empirically Estimating an ABM of School Choice on Household-Level Register Data

The methodological frontier on calibration. Calibrates an ABM of Amsterdam/Almere primary-school choice against confidential CBS register data using neural ratio estimation — a neural-network-based likelihood-free Bayesian estimator that sidesteps the intractable simulator likelihood. Crucially, runs model selection between rational multinomial-logit households and Gigerenzer-style fast-and-frugal heuristic households, and finds heuristics fit register data better. College-monte-carlo currently uses fixed-point iteration against CDS aggregates and a rational-MNL-shaped student utility; both are upgrade paths once student-level data becomes available.

Michailidis, Tasnim, Ghebreab, Santos (2024): Tackling School Segregation with Transportation Network Interventions

A three-layer ABM (residence × transit × schools) where the policy lever is the transit network, not the matching rule. A planner agent — heuristic or reinforcement-learning — chooses transit-network edits to minimise the dissimilarity index, with the RL policy outperforming heuristics on Amsterdam validation data. The college-monte-carlo analog isn't transit infrastructure; it's the simulator's hook multipliers, yield protection, and phantom-applicant scaling, all of which are policy levers an RL designer could optimise over.

Mennle and Seuken (2014): Trade-offs in School Choice — DA vs Naive vs Classic Boston

Theory + simulation comparing three centralized mechanisms. The headline result is that welfare and incentive-compatibility produce exact-reverse orderings: BM rank-dominates ABM rank-dominates DA on welfare under truthful play, but DA is strategy-proof and BM isn't. ABM lies on the Pareto frontier with welfare close to BM and ~50% lower manipulation gain. College-monte-carlo is decentralized rather than centralized, so we can't pick a mechanism — but we can compute the analogous per-cell manipulation gain (truthful vs strategic preference-list construction by archetype × tier), which is the third Tier-1 extension.

Cross-domain references

Not every paper that informs the simulator is from school choice. Two adjacent-domain references contribute techniques rather than models.

Dickerson, Procaccia, Sandholm (2014): Price of Fairness in Kidney Exchange

Formalises fairness in kidney paired donation: high-CPRA (highly sensitized) patients are systematically underserved by max-weight matching, and the paper introduces lexicographic and α-weighted fairness criteria with price-of-fairness bounds that come in under 5% on UNOS pilot data. The structural analogy to admissions hooks (legacy, athlete, donor, first-gen, Pell, URM, geographic, gender, major) is direct: each hook tilts the matching away from a pure academic-index objective in service of an institutional fairness goal. The natural college-monte-carlo extension is a per-hook ablation that quantifies what each hook costs the admitted-class academic mean — the second Tier-1 narrative extension.

Bao et al. (2025): Timing the Match

Deep Q-learning with potential-based reward shaping (PBRS) learns an adaptive matching-clearing timing policy in NYC ride-hailing, reducing wait time 15–30% over fixed-interval baselines. The methodological precedent: using RL to choose when to clear a market. Admissions has fixed deadlines (ED in November, EDII in January, RD in March), but those deadlines are policy choices, not natural laws. Whether they should be adaptive is a research-grade question; the page above frames it without claiming we'll build it next quarter.

What we're building next

Three of the papers above (Reardon, Dickerson, Mennle-Seuken) point at three concrete extensions that share three properties: zero model changes, zero calibration redo, directly publishable narrative outputs. They are documented in detail in Three counterfactual extensions for college-monte-carlo:

1. Reardon-style mechanism shutoff — turn each SES-linked mechanism off and report the SES-by-tier enrolment gradient delta.
2. Dickerson-style price-of-fairness sweep — ablate each hook's strength from 1.0 → 0.0 and report the admitted-class academic-mean and composition tradeoff.
3. Mennle-Seuken-style manipulation gain — per (archetype × tier) cell, compare student outcomes under truthful vs three strategic preference-list regimes (ED-aggressive, RD-safeties, oracle).

All three are gated by a single COUNTERFACTUAL config object whose strengths default to 1.0 (no-op), with pre-computed JSON written by a new harness mirroring the existing research/calibrate_v*.cjs pattern. The roadmap page has the full design, including the deferred research-grade extensions (Santos RL designer, Dignum NRE, Bao adaptive timing) that require model changes and aren't on the near-term list.

Where the corpus lives

The local mirror at research2/cas-abm-references/ contains:

• 36 synthesis writeups under markdown/ — short reviews of each paper, organized by topic. These are read-only excerpts; the source of truth is the upstream 2,762-paper corpus at ~/Dropbox/experiments/cas-abm/research/, which exports here via a Python script.
• 6 stand-alone Node.js reproductions under reproductions/ — one per Tier-1 paper, each with its own embedded RNG (Mulberry32) and no npm install. Each reproduces the qualitative shape of the paper's headline result on synthetic data; absolute numbers don't match published values, but the structural insight does. The headline result of each is in reproductions/SUMMARY.md.
• PDFs and HTML originals are kept locally but gitignored; re-export them from the source corpus when needed.

The reproductions are written end-to-end as worked examples — each one is intentionally not a shared library, so they can be read straight through and mined for college-monte-carlo extensions. When the roadmap items ship, expect the harness in research/build_counterfactuals.cjs to look more like one of these reproductions than like a refactor of sim.js.