Experiments and “Rational” Behavior, 5/1/07

Beauty Contest Game Each person choose a number from 0 to 100. We will average these numbers. The person closest to 2/3 of the average will win $1.

Experiments and rationality In general, we know that people don’t adhere to the strict definition of rationality. But game theory still usually provides good predictions. Most experiments have been done in economic settings.

Bounded rationality Even in competitive contexts, people often don’t optimize (Herbert Simon). They “satisfice.” Experiments shed light on the “bounds” of rationality.

Ultimatum Game As the experimenter, I give you $1. You must now offer some of this to your partner. If your partner accepts your offer, you split the money as agreed. If your partner rejects the offer, you both get nothing. How much do you offer?

Ultimatum Game Nash equilibrium offer = 0% Outcomes of experiments are 40%-50% Otherwise the offer is rejected The result doesn’t depend on stakes –People in Indonesia and Slovakia were offered several weeks’ wages So, people reject “unfair” offers

Ultimatum Game The definition of “fairness” depends on the institutional context “Primitive” cultures are more likely to play the Nash equilibrium, perhaps surprisingly.

Risk Aversion Consider the following two pairs of choices: –A) $950 or –B) 1 in 10 chance of $10,000 –C) $1050 –D) 1 in 10 chance of $10,000

Risk If you don’t care about risk (risk neutral), you would choose the higher expected payoff in each (B and C) If you are risk averse, you choose the sure thing even if it has a lower expected value (A and C) If you are risk acceptant, you choose the lottery (B and D)

Risk The choice of A and D is inconsistent. This general idea applies to a well-known experimental result, the Allais Paradox

Allais Paradox Choose: –A) $100 or –B) $0 with 1% chance, $100 with 89% chance, $500 with 10% chance –C) $0 with 89% chance and $100 with 11% chance, or –D)$0 with 90% chance and $500 with 10% chance

Allais Paradox Many people (often ~40%) choose A and D. But this is inconsistent with any version of expected utility theory. If you choose A, this means U(100)>.01(U(0))+.89(U(100))+.1(U(500)).11(U(100))-.01(U(0))>.1(U(500)).11(U(100))+.89(U(0))>.1U(500))+.9(U(0))

Allais Paradox But this means that you must prefer C over D, since these are just the expressions for the expected utility of C and D. So choosing both A and D violates expected utility theory, regardless of your attitude toward risk.

Framing Effects Probability of Survival RadiationSurgery After Treatment 100%90% After One Year 77%68% After Five Years 22%34%

Framing Effects Probability of Death RadiationSurgery After Treatment 0%10% After One Year 23%32% After Five Years 78%66%

Framing Effects Experimental Results Survival frame Survival frame Death frame Death frame Radia- tion SurgeryRadia- tion Surgery U.S. doctors 16%84%50% Israeli medical students 20%80%45%56%

Prospect Theory 1.Utility function is steeper in losses than in gains 2.People are risk averse in gains and risk loving in losses

Prospect Theory GainsLosses Value

Prospect Theory 3. People overestimate low probability events and underestimate high probability events

Prospect Theory 0 Objective probability 1 Subjective probability Expected response Observed response

Beauty Contest Revisited How do real people play the beauty contest? The averages we have are for novice groups, who have never seen this game or much game theory before. Also for early rounds of the experiment.

Beauty Contest PopulationApproximate Average Guess UCLA undergraduates41 Pooled average, all undergraduates 33 U. Penn undergrads28 CEOs, Wharton class26 Caltech undergraduates10

Beauty Contest Typically, after about a dozen rounds, most groups learn to play the Nash equilibrium So the averages converge to 0.