Layup Equilibria

An evolutionary game-theoretic model of strategic course selection at Dartmouth. Final project for MATH/QSS 30.04 (Evolutionary Game Theory), Spring 2026.

The compiled paper is in EGT_final_project.pdf. Source is main.tex.

Abstract

Many students at selective universities pick easy courses, often called "layups," mainly to protect their GPA. We model this with evolutionary game theory, treating the student body as a population evolving under replicator dynamics across three behavioral types, purists (s_A = 0.10), balancers (s_B = 0.35), and strategists (s_C = 0.70). Each student's payoff depends on their own layup intensity, the population mean, and a GPA-importance parameter w. Under calibrated competition intensity γ = 3.0, the model predicts that the strategist vertex is the unique strict ESS once w > 2.60. We test four predictions against a survey of n = 51 Dartmouth undergraduates. Three sign-tests hold in the predicted direction but fall short of conventional significance: higher GPA importance tracks with higher layup ratios, GPA-protective course avoidance correlates with both higher s and higher w, and perceived peer pressure correlates positively with s. Career tracks differ in mean layup ratio, but only marginally (F = 2.29, p = 0.062), and the predicted ordering does not hold. Two findings cut sharply against the model. Pre-medical students show one of the lowest observed layup ratios despite the highest w (suggestive only, n = 3), and the empirical population clusters at the balancer vertex rather than the strategist equilibrium predicted at w̄ = 3.59. We discuss explanations and show that eliminating enforced grading medians is predicted to raise, not lower, the equilibrium layup ratio.

Repository layout

.
├── main.tex                          # paper source
├── refs.bib                          # bibliography (APA, biblatex)
├── EGT_final_project.pdf             # compiled paper
├── data/
│   ├── EGT Project (Responses).csv   # raw Google Form export, 51 responses
│   ├── cleaned_responses.csv         # cleaned dataset, 51 rows x 19 columns
│   └── stability_table.csv           # replicator-dynamics eigenvalues at w ∈ {1, 3, 5}
├── notebooks/
│   ├── 01_clean.ipynb                # raw → cleaned dataset
│   ├── 02_empirics.ipynb             # P1–P4 tests, OLS / ANOVA / t-test
│   └── 03_replicator_simplex.ipynb   # replicator dynamics, phase portraits, stability
└── figures/                          # PNG outputs from the notebooks

Data

Three CSV files in data/:

• EGT Project (Responses).csv is the raw Google Form export.
• cleaned_responses.csv is the working dataset. Each row is one respondent. Columns of interest: s (the layup ratio, layups / courses, in [0, 1]), w (GPA importance, 1–5), track (career track: pre-med, finance/consulting, tech/engineering, graduate/PhD, government/nonprofit, undecided), q7_score (GPA-protective course avoidance, 0–2), q9_score (perceived peer pressure toward easy courses, −2 to +2).
• stability_table.csv is the output of the replicator-dynamics eigenvalue analysis at w ∈ {1, 3, 5}.

Notebooks

Run in order:

1. notebooks/01_clean.ipynb. Loads the raw Google Form CSV, normalizes major names, encodes ordinal responses to numeric, computes s, and writes data/cleaned_responses.csv.
2. notebooks/02_empirics.ipynb. Tests the four predictions against the survey. OLS with HC1 standard errors for P1, ANOVA across tracks for P2, t-tests for P3, correlations for P4. Writes figures/desc_overview.png, figures/p2_box_s_by_track.png, figures/p4_scatter_q9_s.png.
3. notebooks/03_replicator_simplex.ipynb. Discrete three-type replicator dynamics with s_A = 0.10, s_B = 0.35, s_C = 0.70 and γ = 3.0. Forward Euler integration on the 2-simplex from a grid of starting points, then eigenvalue analysis at the vertices. Writes figures/simplex_w{1,3,5}.png, figures/simplex_panel.png, figures/empirical_simplex.png, and data/stability_table.csv.

Reproducing the analysis

pip install pandas numpy scipy matplotlib statsmodels
jupyter notebook

Then open the three notebooks and run them in order. Outputs land in data/ and figures/.

License

MIT. See LICENSE.