Game 3: Hedonic sorting

The story

Seventy-five households choose where to live among six locations, A to F. The locations differ in environmental quality (EQ) and in a second amenity (SQ), such as school quality. Location A is free. In the other five, a location’s price depends on how many households live there. Your team plays one household type. In the later rounds the types differ in how much they value environmental quality. Round by round you work out where the households end up and what each location costs.

Join

• Teams: envecon-games.netlify.app/games/hedonics-online/student.html
• Or type envecon-games.netlify.app, then tap Join the sorting game.
• Teams of two or three, at most six teams.
• Type a team name: your first names, for example Giulia Tom. Two teams that type the same name become one team.
• One phone per team submits. A teammate can follow on a second phone by typing the same team name.
• Each team gets a household type in the order it joins. Your phone shows your type.
• If your phone dies or the page closes, rejoin with the same team name.

How we play

• A household’s utility at a location is U = α × EQ + β × SQ − P.
• Prices: location A is free (P = 0) and has room for everyone. In B to F the price equals the number of households that live there.
• Equilibrium: every household lives where its utility is highest, given the prices, and the prices follow the rule above.
• Any household can move to A for free. So a household lives elsewhere only if its utility there is at least as high as in A.
• Each round your phone shows the EQ and SQ of every location. In rounds 1 to 3 the phone also shows one utility formula, the same for every household. In rounds 4a to 5 it shows a table with each type’s α and its number of households.

The rounds

• Rounds 1 to 3: every household has the same tastes, α = 3 and β = 1, whatever type your phone shows. In round 1 the locations differ only in EQ. Round 2 adds a second amenity: the locations differ in EQ and in SQ. In round 3 they still differ in both, but EQ no longer rises from A to F.
• Rounds 4a, 4b and 5: each household type has its own α, and β = 1 for every type. Round 4a has one clean location and round 4b has two. In round 5, EQ rises from A to F. All six types are in the market, even if fewer than six teams play.

What your team submits

Each round your team submits three answers:

1. The number of households in each location, A to F: six whole numbers that add up to 75.
2. The best location for your household type.
3. Your type’s utility at that location.

• Numbers that do not add up to 75 are refused and do not cost an attempt.
• Three wrong submissions lock the round for your team, and your phone then shows the right answers.
• A utility within 0.5 of the right value counts as right.
• If your type is equally well off in several locations, any of them is right.
• When every team is right or locked, every phone shows the round’s market.

Tips

• Work out the prices before you compute utilities. In B to F, each price follows from the number of households in that location.
• Before you submit, check every location: no household there should be able to do better elsewhere at the same prices.
• Nothing is graded and there is no ranking.