Experimental Economics

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Experimental Economics

• NSF short course
• David Laibson
• August 11, 2005

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Outline

• Game theory and behavioral game theory
• Experimental economics and behavioral
  economics
• P-beauty
• Buying a firm

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Game Theory and Behavioral Game Theory

• game theory is a mathematical theory of game
  playing
• game theory is based on the idea that everybody
  maximizes
• behavioral game theory is also a mathematical
  theory of game playing
• behavioral game theory is based on the idea that
  everybody tries to maximize but that people
  sometimes make mistakes
• behavioral game theory is designed to describe
  the behavior of real people

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Experimental Economics and Behavioral Economics

• experimental economics is a research method ---
  research that uses experiments
• behavioral economics studies economic models that
  include psychological factors
• social preferences
• problems of self-control
• limits on rationality

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Experimental Economics

Behavioral
Economics
Today
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P-Beauty ContestRules
Name ________________

• Players choose a number from 0 to 100 (all
  numbers allowed, including decimals).
• I collect all of the chosen numbers.
• I average the numbers. Call the average X.
• I calculate 2/3 of X. Let Y (2/3)X.
• Player whose number is closest to Y wins 20.
• If there is a tie, tied players split the prize.
• Write your chosen number here ______
• On the reverse side, please explain your choice
  

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How would a rational person play?

• A rational player should maximize their winnings
  (i.e., their payoff).
• To be on the safe side, we say that a rational
  player should maximize their average (or
  expected) payoff, since there is sometimes a
  degree of uncertainty.
• Definition In a rational equilibrium, all
  players maximize their expected payoff.

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Lets look for a rational equilibrium.

• What if everyone guessed 0?
• The average guess would be 0.
• Given what everybody else is doing (picking 0),
  the best thing for me to do is also to pick 0,
  since my guess is 2/3 of the average guess.
• So if everyone picks 0, everyone is maximizing
  their expected payoff given what everyone else is
  doing.
• Everyone picking 0 is a rational equilibrium.

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Is there another rational equilibrium?

• What if everyone guessed 10?
• The average guess would be 10.
• Nobody is picking a number that is two-thirds of
  the average (2/3)10. So nobody is maximizing
  their expected payoff.
• Everyone guessing 10 is not a rational
  equilibrium.
• In fact, everyone guessing 0 is the only rational
  equilibrium.

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Do people play a rational equilibrium?

• What do you think?
• Why or why not?
• Average number that you chose 18.3
• Median number that you chose 20
• 2/3 Average Guess 12.19
• So the best guess would have been 12.19
• See histogram for dispersion
• See Nagel (1995) and Bosch-Domenech et al (2002)

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What did you do?

• 1st order reasoning Equal probability
  distribution Eav 50, so 2/350 33.
• 2nd order reasoning I figure most folks will
  assume other folks assume a random distribution
  between 1 and 100 so 2/3 2/3 50 22.
• 8-order reasoning If everyone is seeking to
  optimize their probability, then first the
  average will be 50, 2/3 of that, so everyone will
  pick 33 but if everyone figures that then they'll
  pick 2/3 of that etc...down to 0.
• behavioral game theory everyone will 1st think
  x 50, implying that y 33.3, but then x 33.3
  implying that y 22.2... end up at 0 eventually.
  but don't know how far to go, so i'll guess a low
  nonzero number, 5

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Lessons from p-beauty contest

• Game theory predicts that everyone is equally
  (and perfectly) rational
• But real players are not all perfectly rational
• different education
• different levels of experience
• different types of thinking
• different intensity of thinking

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• If people were all perfectly rational, it would
  be impossible to consistently be one-step ahead
  of the competition, since everyone anticipates
  everyone elses' moves.
• In the real world staying one-step ahead of the
  competition is a reasonable goal (which some
  highly experienced, well informed people will
  achieve).
• But it is also possible to be one-step behind
  the competition (which some less experienced,
  less informed people will achieve).
• Its useful to try to figure out where you stand!

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• Assuming that everyone is rational may not be the
  best strategy in practice.
• However, the rational equilibrium is still a
  useful concept because it gives us information
  about some behavioral tendencies.
• Successful real-world behavior combines an
  appreciation that some opponents will be highly
  rational and other will be a little confused.
• Successful real-world actors never forget to
  consider the possibility that they are themselves
  the confused players.

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IQ, Time, Stakes, Learning

• CalTech students have a median math SAT of 800
  and the average test score of the applicants to
  CalTech is higher than the average test score of
  the students who are accepted at Harvard.
• Nevertheless, CalTech students do not play much
  differently than students at other colleges
• However, we know very little about how people
  without much education play such games.
• Time and stakes make only a small difference.
• Learning makes a large difference. There are no
  interesting games in which subjects reach a
  predicted equilibrium immediately. And there are
  no games so complicated that subjects do not
  converge in the direction of equilibrium with
  enough experience in the lab. (Camerer, 2002)

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Why is it called the p-beauty contest?

• In the General Theory, Keynes describes a
  newspaper beauty contest in which readers guess
  which published photos other readers will pick as
  the most beautiful.
• 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.
• Your challenge was also to select a number that
  reflected your best guess of what other players
  would do (and vice versa).