Experimental Economics NSF short course David Laibson August 11, 2005

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

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

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

Experimental Economics Behavioral Economics Today

P-Beauty Contest Rules 1.Players choose a number from 0 to 100 (all numbers allowed, including decimals). 2.I collect all of the chosen numbers. 3.I average the numbers. Call the average X. 4.I calculate 2/3 of X. Let Y = (2/3)X. 5.Player whose number is closest to Y wins $20. 6.If there is a tie, tied players split the prize. Write your chosen number here: ______ On the reverse side, please explain your choice… Name: ________________

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.

Let’s 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.

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.

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 = So the best guess would have been See histogram for dispersion See Nagel (1995) and Bosch-Domenech et al (2002)

What did you do? 1st order reasoning: “Equal probability distribution: E[av] = 50, so 2/3*50 = 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.” ∞-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 = end up at 0 eventually. but don't know how far to go, so i'll guess a low nonzero number, 5”

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

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). It’s useful to try to figure out where you stand!

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.

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)

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).