Behavioral Game Theory: A Brief IntroductionBehavioral Game Theory and Game PracticeFeeling in ultimatum games: How much do you offer out of $10?How People Ultimatum-BargainUltimatum offer experimental sitesUltimatum Bargaining across CulturesSlide 7Fair offers correlate with market integration (top), cooperativeness in everyday life (bottom)Ultimatum offers across societies (mean shaded, mode is largest circle…)Ultimatum Bargaining across MajorsUltimatum Bargaining and LooksStakes, Entitlement, FramingUltimatum offers of children who failed/passed false belief testSubject (autistic?) complaining post-experiment (Zamir, 2000)Feeling: This is your brain on unfairness (Sanfey et al, Sci 13 March ’03)Limited equilibration Beauty contest gameSlide 17Beauty ContestIterated DominanceA New Theory…A New Theory of UtilityInequality AversionInequality Aversion: AdvantagesInequality Aversion on GraphsBehavioral Game Theory:A Brief IntroductionNetworked LifeCSE 112Spring 2005Prof. Michael KearnsSupplementary slides courtesy of Colin Camerer, CalTechBehavioral Game Theoryand Game Practice•Game theory: how rational individuals should behave•Who are these rational individuals?•BGT: looks at how people actually behave–experiment by setting up real economic situations–account for people’s economic decisions–don’t break game theory when it works•Fit a model to observations, not “rationality”Feeling in ultimatum games: How Feeling in ultimatum games: How much do you offer out of $10? much do you offer out of $10? Proposer has $10Proposer has $10Offers x to Responder (keeps $10-x)Offers x to Responder (keeps $10-x)What should the Responder do? What should the Responder do? Self-interest: Take any x>0Self-interest: Take any x>0Empirical: Empirical: Reject x=$2 half the time Reject x=$2 half the timeHow People Ultimatum-BargainThousands of games have been played in experiments…•In different cultures around the world•With different stakes•With different mixes of men and women•By students of different majors•Etc. etc. etc.Pretty much always, two things prove true:1. Player 1 offers close to, but less than, half (40% or so)2. Player 2 rejects low offers (20% or less)Ultimatum offer experimental sitesUltimatum Bargaining across Cultures Sharing norms differ in the industrialized worldJapan, Israel lowest (Roth et al. 1991)Machiguenga farmers in Peru (Henrich 2000)Offered 26% on average, accepted all but 1 offerVery socially disconnectedAche in Paraguay, Lamelara in IndonesiaMade hyperfair (more than 50%) offers Headhunters (potlatch culture), whalersslash & burngathered foodsfishinghuntingThe Machiguengaindependent familiescash croppingFair offers correlate with market integration (top), Fair offers correlate with market integration (top), cooperativeness in everyday life (bottom)cooperativeness in everyday life (bottom)Ultimatum offers across societies Ultimatum offers across societies (mean shaded, mode is largest circle…)(mean shaded, mode is largest circle…)Ultimatum Bargaining across Majors Economics majors offer 7% less, accept 7% less(Carter and Irons 1991)They must have learned game theory!… but this behavior is consistent across years of study (freshman to seniors) … maybe their game-theoretic nature made them want to study economics?Other studies show no correlation, or that econ/business students offer more.Ultimatum Bargaining and Looks70 University of Miami students, photographed and rated for attractiveness (Schweitzer and Solnick 1999)Man as player 1, attractive woman as player 2…Doesn’t make much differenceWoman as player 1, attractive man as player 2…Average offer is 50.7% (hyperfair!)Small percentage (1 or 2?) offer almost everythingStakes, Entitlement, FramingIndonesia: from a day’s wages to a month’s wagesNo difference…Florida: answer questions to get $400 pie instead of $20More low offers at $400 … but subjects earned itFraming it as a buyer/seller exchange lowers offers 10%Framing it as a resource competition raises them slightly(Hoffman et al. 1994)Ultimatum offers of children who Ultimatum offers of children who failed/passed false belief testfailed/passed false belief testSubject (autistic?) complaining post-Subject (autistic?) complaining post-experiment (Zamir, 2000)experiment (Zamir, 2000)Feeling: This is your brain on unfairnessFeeling: This is your brain on unfairness(Sanfey et al, Sci 13 March ’03)(Sanfey et al, Sci 13 March ’03)1.1.Limited equilibrationLimited equilibrationBeauty contest gameBeauty contest gameN players choose numbers xN players choose numbers xii in in [0,100][0,100]Compute target (2/3)*(Compute target (2/3)*( x xii /N) /N)Closest to target wins $20Closest to target wins $2000.050.10.150.20.250.30.350.4191 72 53 34 14 95 76 57 38 18 99 7num ber choicesp r e d ic t e d f r e q u e n c yBeauty contest results (Expansion, Financial Times, Spektrum) 0.000.050.100.150.20numbersrelative frequencies225010033average 23.070Beauty ContestSome number of players try to guess a number that is 2/3 of the average guess.The answer can’t be between 68 and 100 - no use guessing in that interval. It is dominated.But if no one guesses in that interval, the answer won’t be greater than 44.But if no one guesses more than 44, the answer won’t be greater than 29…Everyone should guess 0! And good game theorists would…But they’d lose…Iterated DominancePeople don’t instantly compute all the way to 0The median subject uses 1 or 2 rounds of iteration (25, 35)Guessing 0 on the first round (game theorist) is poorGuessing 30 (behavioral game theory) is much betterBut 30 isn’t a good guess the seventh time you play…A New Theory…We could create new per-game theories…But this would be useless.We could consider these as repeated games of some sort…But that complicates a lot of things.Maybe we can make a small change to something underlying…What if people don’t only care about their own payoffs?A New Theory of UtilityConsider that people still like their payoffsThey also dislike others having more money, with some coefficient .And they dislike having more money than others, with coefficient .U_1 is player 1’s utility; P_1 & P_2 are the players’ payoffs.U_1 = P_1 - (max[P_2 - P_1, 0]) - (max[P_1 - P_2,0]) is “envy” is “guilt”0 <=  < 1  < Different players can have different  and Inequality AversionU_1 =