Beauty Contest Game, explained.
The Beauty Contest Game asks players to predict other players' expectations. In this version, the target is two-thirds of the average number chosen by the group.
Why it happens
A sensible guess depends on how far others reason about one another. Starting from a guess near fifty, one reasoning step suggests roughly thirty-three, another roughly twenty-two, and so on. The depth assumed for others matters.
Keynes's beauty-contest metaphor describes decisions about other people's expectations. Later experiments turned the idea into number-guessing games.
Read the result
Move the opponent reasoning-depth control and compare your guess with the resulting target. Your own guess also changes the group's average, so the best response is not simply two-thirds of an average that excludes you.
A worked example
Reasoning about a group's guesses
If everyone else begins near fifty, a lower number near two-thirds of that value looks promising.
If others anticipate the same adjustment, the likely average falls and the useful guess falls with it.
Prediction requires an assumption about actual opponents, not only a chain of increasingly sophisticated calculations.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Nine opponents each guess near 50×(2/3)^depth with seeded noise of at most 5 points. Your target is (2/3) times the average of all ten guesses, including your own. The chart shows how close each possible guess gets to its resulting target. Best response solves guess=(2/3)×(sum of opponents+guess)/10.
Where this idea is useful
A practical use
When estimating resale value, what others will pay can matter separately from your own private use value.
A common misconception
“The deepest reasoning always wins.”
A guess can be too low when other players use shallower reasoning. Performance depends on the group you actually face.
What this explanation leaves out
- The bots use a chosen rule, not measured human thinking. Repeated play with real people can change expectations, and this single-round game is not a market forecast.
How does this relate to Keynes's metaphor?
Keynes described choices influenced by expectations of what other people would favor. The later number game isolates that recursive-expectation idea; it is not a complete model of financial markets.
Are you predicting the object's value or what others believe others will choose?
Associated thinkers
Further reading
Explore the original research or the teaching reference behind this experiment.