Case 01 — Pricing Tickets for UT Austin Football Games

Background

Your team is advising the UT Austin athletic department on ticket pricing for upcoming football games. Tickets are sold in three tiers — Low, Medium, and High — each with its own price and its own fixed seating capacity.

The department has historical sales data from past games: the prices charged in each tier, the number of tickets sold in each tier, characteristics of the game, and total revenue. Your job is to use that data to recommend prices for three upcoming games.

The Decision Problem

You must recommend a price for each of the three tiers for each of three upcoming games:

These games differ in opponent strength, timing within the season, and proximity to holidays — all of which plausibly shift demand. A single pricing recommendation applied uniformly across all three is unlikely to be defensible.

What the Historical Data Represents

The provided workbook contains, for each past game: prices by tier, observed sales by tier, game characteristics (opponent, point in season, holiday timing), and realized total revenue. Three features of this data should shape how you use it:

• Censoring. Observed sales are capped at capacity. For sold-out tiers, the true demand was at least the observed number — possibly far more.
• Endogenous prices. Past prices were not set randomly. They were chosen strategically, likely in response to anticipated demand, so price and demand are correlated through the department's own past decisions.
• Tier dependence. The three tiers are not independent markets. A high-demand game lifts all tiers together; substitution across tiers is also plausible. Modeling each tier in isolation discards real structure.

Because of censoring and endogeneity, analyses built on averages or on a single deterministic demand estimate will be misleading. The case is designed to push you toward simulation.

Suggested Analytical Approach

1. Explore the data. Understand the distribution of sales and revenue by tier, how often each tier sold out, and how sales co-move with game characteristics and with each other.
2. Build a baseline (naive) simulation. Start with the simplest possible model — for example, assume future demand looks like the historical average. Then critique it explicitly: what does it get wrong, and why?
3. Build a bootstrapped simulation. Select a relevant subset of historical games, resample rows with replacement, and treat each resampled row as a draw of a possible future game. Resampling whole rows (rather than tiers independently) preserves the correlation across tiers that you observed in the data.
4. Adjust for new prices. A bootstrapped row carries the old price. To evaluate a new price, scale demand using a constant-elasticity adjustment:
   ŝ_k^new = s_k^boot × (p_k^new / p_k^old)^−η_k
   Then enforce the capacity cap on the adjusted quantity, compute revenue, and repeat across many resampled draws to build a revenue distribution.
5. Compare pricing policies. Evaluate candidate price vectors on expected revenue, on downside risk (10th and 25th percentiles), and on the probability of outcomes you care about — sellouts in a tier, or low utilization.

Final Deliverables

What We Are Looking For

• Explicit acknowledgment of uncertainty and of the limitations of your model.
• Use of simulation to reason about distributions of outcomes rather than point averages.
• Clear articulation of the tradeoff between expected performance and risk.
• Communication aimed at a decision-maker: concise, concrete, and honest about what you don't know.