Alan's Economics Commons

Reactions and Equilibrium

Puzzle 1. Race to 7

Two people take turns counting numbers starting from 1. You cannot skip numbers or repeat numbers. On each turn, a player may say one or two consecutive whole numbers. Whoever is first to say 7 wins.

Puzzle 2. Cutting the Cake

Buzz Lightyear and Woody are sharing one big cake. Both want a bigger piece.

Puzzle 3. KFC & McDonald’s

KFC and McDonald’s plan to open their first store on a new street. There are two popular locations:

• Center: the exact middle of the street.
• Side: the point one-quarter along the street.

Both companies must decide at the same time: “Shall we open at Center, or Side?” Neither knows what the other will choose.

Puzzle 4. The Green Eyes

On an island live three people with perfect logic.

Rules:

1. Everyone can see the eye colour of all other people.
2. No one can see their own eye colour.
3. No one on the island may talk about eye colour.
4. All people are perfectly rational. Everyone knows everyone else is perfectly rational.
5. If anyone works out that they have green eyes, they must leave the island at midnight the same day.
6. If they cannot be certain, they stay.

Facts:

• All three islanders have green eyes.
• No one knows their own eye colour.

One day, a visitor comes and speaks publicly to everyone:

“I see at least one person with blue eyes.”

Puzzle 5. The Best Wand

You represent your wizard school in a fight against two other wizards:

• Wizard from Newt-niz School: His wand turns people into fish. Hit rate: 70%.
• Witch from Leib-ton School: Her wand turns people into stone statues. Hit rate: 90%.

The three take turns attacking in this fixed order: You → Newt-niz Wizard → Leib-ton Witch → You → … Anyone who gets hit is out of the fight.

It is your turn first. You must pick one wand from three choices:

A note for the next move

Each puzzle asks the same quiet question: if everyone can react to everyone else, what choice still makes sense? That is where strategic thinking begins.