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Iterative Reasoning

Beauty Contest Experiment

Jacqueline Arevalo

on 5 October 2011

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Transcript of Iterative Reasoning

Iterative Reasoning in the Keynesian Beauty Contest Experiment Introduction The Keynesian beauty-contest game is an experiment on iterative reasoning

How many levels of reasoning are used when going through dominant strategies
Help explain price fluctuations in equity markets The Beauty of it... Intelligence is devoted “to anticipating what average opinion expects the average opinion to be.” Pick out the six prettiest faces from a hundred photographs, the prize being awarded to the competitor whose choice most closely corresponds to the average preferences Choose a Number Rosemarie Nagel designed the well known version in 1995 in which participants choose a number from 0-100.
Whoever is closest to the average of the guesses multiplied by a parameter won
A rational participant would eliminate dominant strategies until only one remains

Nagel’s participants didn't choose the Nash equilibrium of 0
they choose a random strategy, believed that other participants weren't as smart, or didn’t reasoned far into multiple levels. Why a Beauty Contest? familiarity due to behavioral economics see if there were any relationships to reasoning displayed in every day life interest in how it could translate in to everyday life Questionnaires had an ID number that participants were told to be aware of

Each set was handed face down and participants were told simultaneously to flip it over (for simultaneous timing)

First section was a logic question and Nagel’s p-beauty contest. Particpants had five minutes to answer this section
(p = 2/3) Experiment Design 2 Sudoku puzzles were given afterwards (another method of testing iterative reasoning), with 10 minutes to solve them.

Prize was given to the ID number who choose the calculated winning number immediately following the experiment The subject’s ID numbers are listed along with the number of Sudoku boxes completed correctly in column “SD Total Right”, whether or not they successfully answered the logic question in column “Question (Y or N)”, their number choice for the beauty contest game in column “BC Guess”, and their level of iterative reasoning, as derived by the experimenters. Results Logic Question Half of the participants answered logic question correctly

No significant correlation was found between the answer to this question and the number choice in the beauty contest experiment.
None of the participants chose a value higher than 66

Meant all participants had a level of iterative reasoning higher than 0. Those participants which selected a value of 0 most likely did so because they were familiar with the Nash equilibrium value. The number selection Histogram shows a very clear saturation at the lower end of the spectrum of bins, showing that participants struggled somewhat with the puzzle.
- This may be due to difficulty of the puzzles or lack of prior experience Sudoku Puzzle Correlation Mumber of boxes answered correctly correlated with a level of iterative reasoning

R = 0.0837

Three participants who chose 0 struggled with the Sudoku puzzles 2 Discussion A different subject pool would have provided significantly different results
- most of the experimental subjects had experience in behavioral economics.

Logic question was inadequate and confusing
- there were two possible answer choices for this question and half picked the correct answer

Subjects may have had Sudoku experience or the instructions where misleading
- Some individuals only answered a few boxes but accurately choose Nash equilibrium
- Past experience with Sudoku may have lead to better performance on the puzzles instead of the beauty contest Conclusion Due to the circumstances surrounding our experiment, our results were inconclusive.

This experiment will likely be irrelevant to the literature surrounding iterative reasoning.
Adding other treatments that would test individual’s levels of iterative reasoning

The reduction in difficulty of the Sudoku - maybe providing only one Sudoku puzzle or a smaller version

Independent timing of Sudoku puzzles
The use of electronic methods to track individual’s progress would also be a way to acquire more data for analysis. Questions? Jacqueline L. Arévalo, Martin Schwed, Evan Scott, Colton Parnes ... or a lack therof? a normal distribution would have been ideal for these values Works Cited Fung, Matthew. "Developments in Behavioral Finance and Experimental Economics and Post Keynesian Finance Theory." Journal of Post Keynesian Economics 29.1 (2006): 19-39. Print.

Nagel, Rosemaria. "Unraveling in Guessing Games: An Experimental Stuy." The American Economic Review 85.5 (1995): 1313-326. Print.
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