Social Cognition
Beauty Contest Game
Also called: p-beauty contest, guess two thirds of the average, Keynesian beauty contest, guessing game, level-k game
Measure steps of strategic reasoning: participants guess two thirds of the group's average over rounds against simulated players, scored by the first guess and its reasoning step.
4-7 minUntimed
Free to start: 10 free participants per account, then $0.99 per participant for academic research, or any yearly plan. Preview any test free after you sign up.
- Papers, 2021 to 2025
- 63
- Evidence grade
- D
- Registered clinical studies
- 0
What it measures
Measures steps of strategic reasoning. In each round the participant and 9 simulated players pick a number from 0 to 100, and the number closest to two thirds of the average wins points. The main score is the first-round guess, read as steps of reasoning about the others.
Constructs
- Strategic reasoning
- Depth of reasoning about others
- Theory of mind
- Learning from feedback
Research uses
- Behavioral economics research
- Strategic thinking and cognitive ability studies
- Social cognition and theory of mind research
- Within-study group comparison
How the paradigm works
The Beauty Contest Game measures how many steps of reasoning a person applies to what others will do (Nagel, 1995). In each round every player picks a whole number from 0 to 100, and the number closest to two thirds of the average of all the numbers wins the round's points; players equally close share them. If everyone reasoned without limit, every number would fall to 0, but people stop after a few steps: a player who expects others to pick at random, averaging 50, picks about 33; one who expects others to reason that way picks about 22, and so on. The first guess therefore reads as steps of reasoning about others (Nagel, 1995; Bosch-Domènech, Montalvo, Nagel and Satorra, 2002).
More about the paradigm
The participant plays in a group of 10 with 9 simulated players, over 4 rounds by default (1 to 10 as a setting), and sees after each round every number, the average, two thirds of it and the winning number. By default the instructions say the other players are computer programs whose rules are based on how people play; a neutral wording leaves that line out. Each simulated player has a fixed number of steps for the session, a mix with 1.5 steps on average as in the cognitive hierarchy model (Camerer, Ho and Chong, 2004): in round 1, players at step 0 pick at random and a player at step k picks about 50 x (2/3)^k; from round 2 each starts from the last round's average. Their choices vary by up to 15%, and every draw comes from the session's seed. Choices are whole numbers, as in the Financial Times contest that Bosch-Domènech and colleagues analysed, so 0 and 1 are both equilibria. One question on finding two thirds of an average, with feedback, comes first, and there is no time limit. The study decides what the points are worth, and the payment line says whether they are exchanged for money.
The main score is the first guess, made before any feedback, and its step of reasoning: the nearest of 50, 33, 22 and 15 on a log scale, with 4 for four or more steps, 0 and 1 included. Later rounds show how guesses move toward 0 as players see the averages, measured as steps applied to the last average. Lower first guesses go with higher cognitive ability (Burnham, Cesarini, Johannesson, Lichtenstein and Wallace, 2009). People who reasoned further against other people still picked near 33 when told the computer players chose at random (Coricelli and Nagel, 2009), so a guess depends on what the participant expects of the others and comparisons belong between people who saw the same instructions. Scores support research and do not diagnose.
Scores
- First Guessscore
- The number chosen in round 1, from 0 to 100, before any feedback.
- Lower means more steps of reasoning about the others
- First Guess Stepscore
- Steps of reasoning the first guess is closest to: 0 near 50, 1 near 33, 2 near 22, 3 near 15, 4 for four or more.
- Higher means more steps
- Equilibrium First Guess0/1
- 1 when the first guess is 0 or 1, the equilibria with whole numbers.
- Informational
- Mean Guessscore
- The mean of the guesses over all rounds.
- Informational
- Last Guessscore
- The guess in the last round played.
- Informational
- Guess Changescore
- The last guess minus the first; empty with one round.
- Negative means moving toward 0
- Steps From Last Averagescore
- From round 2, the median steps of reasoning applied to the average just seen: log(guess / last average) / log(2/3). Guesses of 0 are left out.
- 1 means guessing two thirds of the last average
- Rounds Woncount
- Rounds where the guess was closest to the target, shared or not.
- Informational
- Points Wonpoints
- Points over all rounds, shares of ties included.
- Informational
- Mean Distance From Targetscore
- Mean distance between the guess and two thirds of the round's average.
- Lower means closer predictions of the group
- Guesses Above 67count
- Guesses above 67, which can never be closer to the target than 67.
- 0 expected; a first guess above 67 is flagged
- Practice Correctflag
- 1 when the question on finding two thirds of an average was answered correctly, 0 when not.
- 1 supports interpretation
- Median Decision Timems
- Median time from a round's screen to Submit, over guesses at or after 100 ms.
- Informational
- Guesses Under 100 mscount
- Guesses submitted less than 100 ms after the round's screen appeared.
- 0 expected
- Roundscount
- Rounds scored.
- Informational
Use and evidence
63 papers from 2021 to 2025 name this task in their title or abstract, up 11% compared with 2016 to 2020. That ranks it 236 of 395 test families in our census. See the counts for every test.
Show the numbers
| Year | Papers |
|---|---|
| 2025 | 17 |
| 2024 | 11 |
| 2023 | 12 |
| 2022 | 12 |
| 2021 | 11 |
| 2020 | 8 |
| 2019 | 17 |
| 2018 | 13 |
| 2017 | 7 |
| 2016 | 12 |
| 2015 | 10 |
| 2014 | 11 |
| 2013 | 6 |
| 2012 | 6 |
| 2011 | 7 |
| 2010 | 14 |
| 2009 | 12 |
| 2008 | 8 |
| 2007 | 7 |
| 2006 | 4 |
| 2005 | 8 |
| 2004 | 3 |
| 2003 | 1 |
| 2002 | 3 |
| 2001 | 3 |
| 2000 | 0 |
Use grade D
30 to 99 papers from 2021 to 2025.
Evidence grade D
Little published measurement evidence found.
- Papers on test-retest reliability
- 0
- Papers on reliability or validity
- 3
- Registered clinical studies using it as an outcome
- 0
How the grades work
Use: A is 1,000 or more papers from 2021 to 2025, B 300 to 999, C 100 to 299, D 30 to 99 and E fewer than 30. Evidence: A means at least 25 papers report its test-retest reliability and at least 25 registered clinical studies use it as an outcome; B, at least 8 test-retest papers, and either 5 registered clinical studies or 150 reliability or validity papers; C, at least 2 test-retest papers, 30 reliability or validity papers or 3 registered clinical studies; D, little published measurement evidence found. The counts measure use. They include every paper that names the task in its title or abstract. Grades describe the published research on this task, not ConductCognition's version of it.
Source: ConductCognition test census 0.14.0, counted 31 October 2026 from OpenAlex and ClinicalTrials.gov.
Task design
The trial sequence as the test runs in ConductCognition.
- Group
- The participant and 9 computer programs whose rules are based on how people play. The standard instructions say so; a neutral wording leaves that line out.
- Rule
- Each player picks a whole number from 0 to 100. The number closest to two thirds of the average of all 10 wins the round's points; players equally close share them.
- Simulated players
- Steps of reasoning fixed for the session, 9 times the shares of the cognitive hierarchy model with 1.5 steps on average, rounded: 2 players at step 0, 3 at step 1, 2 at step 2 and 2 at step 3. In round 1, step 0 picks at random and step k about 50 x (2/3)^k; later rounds start from the last average. Each choice varies by up to 15%, drawn from the session's seed.
- Rounds
- 4 (standard; 1 to 10) with the same group, each followed by every number, the average, two thirds of it and the winning number.
- Check
- One question with feedback before the first round: two thirds of an average of 90.
- Points
- 100 per round (standard; 1 to 1,000). Points are hypothetical by default; a setting changes the instruction line to say the study pays.
- Scores
- The first guess, made before any feedback, and its step of reasoning: the nearest of 50 x (2/3)^k on a log scale, from 0 to 4 or more. Also how the guesses moved over the rounds and the points won.
Nagel (1995) ran groups of 15 to 18 students, all of them people, who could pick any number from 0 to 100. Here the other nine players are computer programs, the instructions say so by default, and choices are whole numbers, as in the Financial Times contest that Bosch-Domènech and colleagues (2002) analysed. A guess depends on what a participant expects of the others, so compare people who saw the same instructions. The scores support research and do not diagnose.
Quality checks
Each session is marked valid, needs review or invalid, with the reason, before you see its scores.
Scored rows: the scored run's guesses, one whole number from 0 to 100 per round. No number is correct in advance, so accuracy is not judged against chance, and repeating a number is accepted. A run without the first round's guess is invalid; a run short of its planned rounds, a first guess above 67 and a wrong practice answer are flagged for review. Guesses under 200 ms on at least half the rounds invalidate.
Why these rules
There is no correct option to compare with chance, so accuracy is not judged against chance. The winning number depends on everyone's choices, so a guess is a judgment about the other players, not a right or wrong answer. The first guess, made before any feedback, is the main score, so a run without it cannot be scored. Two thirds of 100 is 66.67, so a guess above 67 can never be closest; as a first guess it often means the rule was misread, but it can be a real choice, so it is flagged and never excludes. An answer under 200 ms is faster than a simple visual reaction, so it cannot reflect the item. Following response-time effort screening for untimed tests (Wise and Kong 2005), the session is invalid only when at least half the answers are that fast.
No percentile. Scores and quality flags only.
Running this test
Settings you can change
| Setting | Standard | Allowed |
|---|---|---|
| Rounds | 4 | 1 to 10 |
| Points per round | 100 | 1 to 1,000 |
| Player wording | Computer programs (standard) | Computer programs (standard), Neutral: the other players |
| Payment line | Hypothetical points (standard) | Hypothetical points (standard), The study pays for points |
Yearly plans can change settings within these limits. Free and pay-as-you-go studies use the standard settings.
Need a setting this test does not have?
Devices and languages
- Untimed test: runs on desktops, laptops, tablets and phones. Participant devices
- Languages: English, Spanish, French, German, Italian, Portuguese (Brazil), Chinese (Simplified) and Japanese.
- Available on: Every plan, including the free plan.
- No percentile. Scores and quality flags only. How norms work
- Recruiting online? See the setup guides for Prolific, Sona Systems, CloudResearch Connect and Qualtrics.
Cite and describe
Participants completed the Beauty Contest Game in a web browser (ConductCognition task version 1.0.0, scoring version 1.0.0; Nagel R, 1995), with the standard settings (rounds: 4; points per round: 100; player wording: Computer programs; payment line: Hypothetical points). The main score was first guess (the number chosen in round 1, from 0 to 100, before any feedback).
ConductCognition versions: task version 1.0.0, scoring version 1.0.0. Every export records the versions each session used, for a methods section.
- Nagel, R. (1995). Unraveling in guessing games: An experimental study. American Economic Review, 85(5), 1313-1326.
- Bosch-Domènech, A., Montalvo, J. G., Nagel, R., & Satorra, A. (2002). One, two, (three), infinity, ...: Newspaper and lab beauty-contest experiments. American Economic Review, 92(5), 1687-1701. https://doi.org/10.1257/000282802762024737Steps of reasoning in large samples, and whole-number choices.
- Camerer, C. F., Ho, T.-H., & Chong, J.-K. (2004). A cognitive hierarchy model of games. Quarterly Journal of Economics, 119(3), 861-898. https://doi.org/10.1162/0033553041502225The mix of reasoning steps the simulated players follow.
- Coricelli, G., & Nagel, R. (2009). Neural correlates of depth of strategic reasoning in medial prefrontal cortex. Proceedings of the National Academy of Sciences, 106(23), 9163-9168. https://doi.org/10.1073/pnas.0807721106Playing against computer players.
- Burnham, T. C., Cesarini, D., Johannesson, M., Lichtenstein, P., & Wallace, B. (2009). Higher cognitive ability is associated with lower entries in a p-beauty contest. Journal of Economic Behavior & Organization, 72(1), 171-175. https://doi.org/10.1016/j.jebo.2009.05.015First guesses and cognitive ability.
Source papers
- Nagel (1995): first-round choices cluster around steps of reasoning from 50, and later rounds move toward 0. Bosch-Domènech, Montalvo, Nagel and Satorra (2002): the same steps in newspaper contests with thousands of readers.Paradigm source, Adults
Questions
How long does the Beauty Contest Game take?
About 4 to 7 minutes, as listed in the test library.
What device does a participant need?
Untimed test: runs on desktops, laptops, tablets and phones. The browser must be Chrome, Edge, Firefox or Safari.
What scores does it produce?
First Guess, First Guess Step, Equilibrium First Guess, Mean Guess, Last Guess, Guess Change, Steps From Last Average, Rounds Won, Points Won, Mean Distance From Target, Guesses Above 67, Practice Correct, Median Decision Time, Guesses Under 100 ms and Rounds. Each session is also marked valid, needs review or invalid, with the reason.
How widely is the Beauty Contest Game used in research?
63 papers from 2021 to 2025 name it in their title or abstract, up 11% compared with 2016 to 2020. That ranks it 236 of 395 test families in the ConductCognition test census (use grade D). Source: ConductCognition test census 0.14.0, counted 31 October 2026 from OpenAlex and ClinicalTrials.gov.
How much reliability evidence does the Beauty Contest Game have?
In the published research, 0 papers report its test-retest reliability and 0 registered clinical studies use it as an outcome (evidence grade D in the ConductCognition test census).
Does it report a percentile?
No. Scores and quality flags only.
Which settings can a researcher change?
Rounds (1 to 10), points per round (1 to 1,000), player wording (Computer programs (standard), Neutral: the other players) and payment line (Hypothetical points (standard), The study pays for points). Settings can be changed on yearly plans; free and pay-as-you-go studies use the standard settings.
Which languages can participants use?
Participants can take this test in English, Spanish, French, German, Italian, Portuguese (Brazil), Chinese (Simplified) and Japanese. English is on every plan, and the other languages come with yearly plans. Have a native speaker read the machine-translated text before launch.
Is this a clinical test?
No. ConductCognition is for research use only. It runs, scores and exports the test; clinical interpretation is outside the platform.
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