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## Keynes P Beauty Contest

This is something I use in my Behavioural Economics course which usually displays interesting results.

Economist John Maynard Keynes described the action of rational agents in a market using an analogy based on a fictional newspaper contest, in which entrants are asked to choose from a set of six photographs of women that are the “most beautiful.” Those who picked the most popular face are then eligible for a prize.

A naive strategy would be to choose the face that, in the opinion of the entrant, is the most beautiful. A more sophisticated contest entrant, wishing to maximize the chances of winning a prize, would think about what the majority perception of beauty is, and then make a selection based on some inference from his knowledge of public perceptions. This can be carried one step further to take into account the fact that other entrants would each have their own opinion of what public perceptions are. Thus the strategy can be extended to the next order and the next and so on, at each level attempting to predict the eventual outcome of the process based on the reasoning of other rational agents.
“It is not a case of choosing those [faces] that, to the best of one’s judgment, are really the prettiest, nor even those that average opinion genuinely thinks the prettiest. We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be. And there are some, I believe, who practice the fourth, fifth and higher degrees.” (Keynes, General Theory of Employment Interest and Money, 1936).

The Game
•Players choose a number from 0 to 100 (all numbers allowed, including decimals). •Teacher collects all of the chosen numbers.
•Teacher averages the numbers. Call the average X.
•Teacher calculates 2/3 of X. Let Y = (2/3)X.
•Player whose number is closest to Y wins a prize.
•If there is a tie, tied players split the prize.