When College Choices Create Congestion, Clearing the Queue Can Come at a Cost

When applicants flock to the same college, they compete for a limited number of places. Shifting some of them elsewhere might raise the chance of an offer at the popular college, but it can also intensify competition at other colleges and prevent people from pursuing their preferred options.

In Discrete Choice under Congestion: Equilibrium and Welfare, Debopam Bhattacharya of the University of Cambridge and Matias Makiranta of the University of Helsinki develop a way to study that trade-off. They combine a general economic model with simulations based on Cambridge undergraduate application records. The paper is an arXiv preprint submitted on 5 November 2026; the landing page does not report journal acceptance.

A stable outcome, under conditions

The authors model people choosing among discrete alternatives whose attractiveness depends on how many others choose them. Their equilibrium is a set of choice shares consistent with the shares people anticipate when making their decisions.

They prove that an equilibrium exists and is unique under a condition they call relative congestion dominance: when demand shifts toward a group of alternatives, those alternatives become no more attractive relative to the options outside the group. The result also requires conditions including continuity, correctly anticipated shares and no exact ties in individual preferences. It allows congestion at one option to affect the payoff from another, provided the relative-dominance condition holds.

The distinction matters for policy simulations. If a model had several possible equilibria after a change, knowing preferences would not by itself select one predicted outcome. Uniqueness supplies a single equilibrium within the authors' assumptions; it does not establish that those assumptions hold in every setting.

Learning from Cambridge choices

The empirical application uses administrative data on 25,325 UK-based applicants from 2013 through 2017, across economics, engineering, mathematics, law, medicine and natural sciences. In the setting studied, an applicant generally applies through one Cambridge college. Colleges differ in attributes such as rent and distance to a department, and capacity varies by college and subject. Some unsuccessful applicants can be admitted elsewhere through a pool, which the empirical choice specification does not model separately.

The researchers estimate preferences separately for men and women, using college and applicant characteristics alongside offer rates. Their theoretical identification argument uses differences across subjects: some college features remain common while subject-specific characteristics and congestion vary. It can recover certain welfare comparisons without specifying a full parametric distribution of preferences, but only under demanding support, rank and other assumptions. Choice data do not identify every possible welfare effect: changing an individual characteristic, for example, can alter utility levels in ways that observed choices alone cannot reveal.

For the actual Cambridge calculations, the authors use a multinomial logit model with a specified distribution of unobserved preference shocks. They use observed choice shares in estimation and solve for a new equilibrium when simulating the rent intervention. Applicants in the estimates favor, among other things, colleges closer to their departments; higher rent is associated with lower attractiveness. The calculations hold capacity fixed and should be read as short-run, model-based counterfactuals, not as outcomes of policies that were implemented.

Choice versus congestion

The first simulation replaces college choice with random assignment in proportion to capacity. The model predicts a welfare loss for everyone: although assignment reduces congestion at some popular colleges, the chance of being assigned there falls in exactly the offsetting proportion. In the paper's capacity-to-applicant offer-rate model, that cancellation leaves the probability of reaching each college unchanged while removing the ability to choose.

The authors express welfare in weekly-rent equivalents: the rent reduction that would compensate an applicant for the change. The estimated median loss is £94.84 per week for men and £61.54 for women. These are measures of valued welfare, not observed rent payments. The conclusion depends on the particular random-assignment and admissions assumptions; it is not a result about every centralized admissions system.

The second simulation raises weekly rent by £100 at King's and Trinity, deliberately taking the policy outside the observed range used for estimation. Some applicants are predicted to leave those colleges, improving offer prospects for those who remain but changing congestion elsewhere. The model produces both winners and losers: the median effect is a £98.27 weekly-rent-equivalent loss for men and a £27.59 gain for women. The authors say the gender difference cannot be attributed to a single cause.

These numbers depend on the assumed preferences, admissions probabilities and equilibrium responses, especially because the simulated rent increase is large. The paper also develops a theoretical extension for people who misperceive success probabilities; it does not estimate an information campaign's effects in the Cambridge application. Its broader message is that relieving one bottleneck is not enough to determine who benefits: the value of choice and the movement of congestion across alternatives matter too.