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The Keynesian Beauty Contest

Keynes (1936): Don't pick what YOU think is best—pick what you think OTHERS think is best. In this game, choose a number from 0-100. The winner is closest to 2/3 of the average. Logical conclusion: everyone should pick 0. Reality: they don't. Why?

🎯 The Guessing Game

Pick a number from 0 to 100:
The winner is closest to 2/3 of the average of all guesses

Levels of Strategic Reasoning

L0
"I'll just pick randomly..." → Average = 50
50
L1
"Others will pick ~50, so I'll pick 2/3 of that"
33
L2
"They'll think like L1 and pick 33, so I'll pick..."
22
L3
"They'll be L2 thinkers, so I'll go one level deeper"
15
L∞
"Following this logic to infinity..." → Nash Equilibrium
0
Your Guess
33
2/3 of Average
22
Winning Guess
24
All 50 Guesses (your guess highlighted):

📊 Game Statistics

Total Players
50
Average Guess
—
Target (2/3 × Avg)
—
Your Distance from Target
—
Nash Equilibrium
0
The only "rational" answer—but real players average 22-33!
"It is not a case of choosing those which are really the prettiest... We have reached the third degree where we devote our intelligences to anticipating what average opinion expects the average opinion to be."
— John Maynard Keynes, 1936

Why Don't People Pick Zero?

📰 Keynes's Original Analogy

Keynes described a newspaper contest where readers voted for the six most attractive faces from 100 photographs. The prize went to those who picked the most POPULAR faces. Smart contestants don't pick what THEY find attractive— they pick what they think OTHERS will find attractive. And smarter ones think about what others think others think...

📉 Stock Market Implications

Keynes argued stock prices aren't determined by "fundamental value" but by what investors think OTHER investors think the price should be. This creates bubbles: everyone buys because they expect others to buy, regardless of underlying value. The beauty contest explains speculation and market psychology.

🧠 Bounded Rationality

Real humans don't iterate to infinity. Studies show most people think 1-3 levels deep: "Others are random (L0), so I'll guess 33 (L1)" or "Others will think like that, so I'll guess 22 (L2)." Very few reach L4+. This is cognitive hierarchy theory—bounded strategic reasoning.

🎲 Experimental Results

In published experiments, winning guesses cluster around 13-22. Financial Times readers: winning guess was 13. Caltech students: average 26. With repetition, guesses converge toward 0—but never reach it. Perfect rationality requires assuming everyone else is also perfectly rational.

♟️ Game Theory Insight

Zero is the only Nash Equilibrium—a state where no player benefits by changing their strategy. But reaching it requires common knowledge of rationality: I'm rational, I know you're rational, I know you know I'm rational... ad infinitum. Humans don't have this.

🌍 Real-World Applications

Speculative bubbles: Buy because others will buy. Voting: Vote for who you think will win, not who you prefer. Fashion: Wear what you think others will think is stylish. Technology adoption: Use what you expect others to use. The beauty contest is everywhere coordination matters.