Splitting the Rent

Envy-free prices for rooms

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Envy-free: everyone prefers their own room at its price.
• With two people there’s a range of envy-free prices; equal surplus picks one.
• Envy-free rent splits exist for any number of people (Su, via Sperner’s lemma).

Steps

1. Two rooms, one rent
2. Set the price
3. Bob’s limit
4. More flatmates
5. Swap the rooms?
6. Stronger preferences