Beauty Contest Foundation

Keynes (1936)

In The General Theory, John Maynard Keynes described a newspaper competition: readers picked the six prettiest faces from a hundred photographs; the prize went to whoever's picks were closest to the population average. Keynes observed:

"It is not a case of choosing those which, to the best of one's judgment, are really the prettiest, nor even those which 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."

This is the recursive logic of every coordination game without a focal "correct" answer. CashPop implements this directly: there is no true answer to the Round question — only the answer most players believe most players will pick.

Stahl & Wilson level-k

Stahl & Wilson (1995) introduced level-k reasoning as a finite-depth model of strategic thought. Each player's strategy depends on their assumed level of strategic sophistication:

• Level-0 plays randomly or by salience (e.g., the answer that "feels right").
• Level-1 assumes everyone else is level-0 and best-responds to that distribution.
• Level-2 assumes everyone else is level-1 and best-responds.
• ...and so on.

In any real population, the mixture of level-0, level-1, level-2, ... is what determines the equilibrium. Different populations have different mixtures: experts trend higher-level; novices trend level-0/level-1.

CashPop's recurring Round structure lets us directly observe and estimate this level-k mixture across millions of Rounds and millions of players. This is the first time the level-k model has been measurable at population scale outside controlled lab experiments (typically 30–200 subjects).

Schelling focal points (1960)

Schelling (1960) observed that in pure coordination games without communication, people converge on focal points distinguished by salience: cultural, linguistic, aesthetic, or contextual.

His classic example: "If you must meet a stranger in New York City tomorrow and cannot communicate, where and when do you go?" A surprising number of respondents — without any prior coordination — name Grand Central Station at noon. This is not because Grand Central is the best meeting place; it is because Grand Central is distinguished in the shared mental model.

CashPop's question reservoir deliberately probes focal-point structure across demographic, cultural, and linguistic groups. Question batteries are designed to detect:

• Cross-cultural focal point divergence ("most popular dessert" — answers differ by region).
• Within-culture focal point stability ("favorite weather" — answers cluster).
• Generational focal point drift ("most fashionable color" — answers shift over time).

What CashPop adds to the literature

Property	Lab studies	CashPop
Subject count	30–200	10,000+ per Round, ~1B over a year
Cultural diversity	Limited to recruiter's reach	6 continents, 8 languages
Real-time observation	Months / years to publish	Live + quarterly aggregated
Incentive compatibility	Often $5–20 lab payment	Real ad-revenue-funded payouts
Reproducibility	Bound by recruiting	Reservoir is publicly auditable, anyone can replicate

The protocol is, in effect, an always-on planetary-scale Beauty Contest measurement instrument.

Equilibrium notes

The Beauty Contest equilibrium under common knowledge of rationality collapses to the lowest-salience answer (everyone reasons to the deepest level, infinitely). In practice, this never happens — finite level-k reasoning means equilibria are mixtures, not corners. The CashPop reward structure (prize-pool proportional, not winner-take-all) does not select for deepest-level reasoning — it selects for being on the modal side. This keeps the game accessible to level-1 and level-2 players, which is most of the population, and prevents the game from degenerating into an experts-only equilibrium.

References

• Keynes, J.M. (1936). The General Theory of Employment, Interest and Money. Chapter 12.
• Stahl, D.O., Wilson, P.W. (1995). On Players' Models of Other Players. GEB 10.
• Camerer, C., Ho, T.-H., Chong, J.-K. (2004). A Cognitive Hierarchy Model. QJE 119.
• Schelling, T.C. (1960). The Strategy of Conflict. Harvard.
• Mehta, J., Starmer, C., Sugden, R. (1994). The Nature of Salience. AER 84.