Prevolio
Game theoryClassroom · multi-user

Keynesian Beauty Contest — Guess ⅔ of the Average

Everyone secretly picks a number 0–100; whoever lands closest to two-thirds of the class average wins. Watch guesses spiral toward zero.

You’ll learn: See why 'everyone is rational and knows everyone is rational' fails in practice, and how strategic reasoning deepens across rounds.

Teacher guide

Students will learn to

  • Experience how guessing the average depends on guessing what everyone else will guess.
  • Connect the Nash equilibrium (everyone guesses 0) to what actually happens in a real room.
  • See strategic learning: guesses fall round over round as players reason one step further.

Before the session — ask

  • If everyone were perfectly rational, what number should they all pick — and why?
  • Do you expect the class to actually land on that number in round one?

After the session — discuss

  • How far was the first-round target from zero, and how did it move across rounds?
  • Why don't real people jump straight to the equilibrium even when they can work it out?
  • What does this say about assuming everyone is fully rational in markets?

Timing

  • Briefing & the rules3–5 min
  • Five guessing rounds6–10 min
  • Debrief & discussion8–10 min

Run it with your class

Students join with a code or QR — no account needed. Teachers start a session from the dashboard.

Join with a codeFor teachers

What is the Keynesian beauty contest?

The Keynesian beauty contest is a game that reveals the limits of assuming everyone is perfectly rational. Everyone secretly picks a number from 0 to 100, and whoever is closest to two-thirds of the group's average wins. Reasoning it through: if you expect the average to be 50, you should guess about 33; but if everyone thinks that, the average is 33, so you should guess about 22; and that logic keeps going down. Following it all the way, the only fully rational outcome — the Nash equilibrium where no one wants to change — is everyone guessing zero. Yet in real games the winning number is rarely zero; it's usually somewhere in the teens or twenties. That gap is the point. Winning doesn't come from being the most rational; it comes from correctly guessing how many steps of reasoning others will actually do — level-k thinking, where level 0 guesses randomly, level 1 best-responds to level 0, and so on. The name comes from Keynes's analogy to picking not the face you find prettiest, but the one you think others will pick. It captures why markets and elections can turn on beliefs about others' beliefs rather than fundamentals.

How the simulation shows it

Everyone secretly picks a number 0–100, and whoever lands closest to two-thirds of the average wins. Playing across rounds shows guesses spiral downward as players anticipate each other — but the winner isn't whoever guessed zero; it's whoever best judged how far everyone else would actually reason.

Common misconceptions

Frequently asked questions

What is the Keynesian beauty contest?
A game where everyone picks a number 0–100 and the winner is closest to two-thirds of the average. It exposes the gap between perfect rationality and how people actually reason strategically.
What is the Nash equilibrium?
Everyone guessing zero. If all players reasoned infinitely, each undercutting two-thirds of the others' guesses, the numbers spiral down to zero — but real play rarely reaches it.
Why isn't the winning number zero?
Because real players do only a step or two of reasoning, not an infinite chain. The average stays well above zero, so the winning guess is usually in the teens or twenties.
What is level-k reasoning?
A model of bounded strategic thinking: a level-0 player guesses randomly, a level-1 player best-responds to level 0, level 2 to level 1, and so on. Winning means judging others' level correctly.
Why is it named after a beauty contest?
Keynes compared investing to a newspaper contest where you pick not the face you find prettiest, but the one you think others will pick — choosing based on others' expected choices, as in this game.

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