Behavioral Game Theory: A Brief Introduction

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Behavioral Game TheoryA Brief Introduction

• Networked Life
• CSE 112
• Spring 2005
• Prof. Michael Kearns
• Supplementary slides courtesy of Colin Camerer,
  CalTech

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Behavioral 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 peoples economic decisions
• dont break game theory when it works
• Fit a model to observations, not rationality

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Feeling in ultimatum games How much do you offer
out of 10?

• Proposer has 10
• Offers x to Responder (keeps 10-x)
• What should the Responder do?
• Self-interest Take any xgt0
• Empirical Reject x2 half the time

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How People Ultimatum-Bargain

• Thousands 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
• Player 1 offers close to, but less than, half
  (40 or so)
• Player 2 rejects low offers (20 or less)

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Ultimatum offer experimental sites
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Ultimatum 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 disconnected
• Ache in Paraguay, Lamelara in IndonesiaMade
  hyperfair (more than 50) offers Headhunters
  (potlatch culture), whalers

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The Machiguenga independent families cash
cropping
slash burn gathered foods fishing hunting
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Fair offers correlate with market integration
(top), cooperativeness in everyday life (bottom)
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Ultimatum offers across societies (mean shaded,
mode is largest circle)
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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.

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Ultimatum Bargaining and Looks

• 70 University of Miami students, photographed and
  rated for attractiveness (Schweitzer and Solnick
  1999)
• Man as player 1, attractive woman as player 2
• Doesnt make much difference
• Woman as player 1, attractive man as player 2
• Average offer is 50.7 (hyperfair!)Small
  percentage (1 or 2?) offer almost everything

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Stakes, Entitlement, Framing

• Indonesia from a days wages to a months wages
• No difference
• Florida answer questions to get 400 pie instead
  of 20
• More low offers at 400 but subjects earned it
• Framing it as a buyer/seller exchange lowers
  offers 10
• Framing it as a resource competition raises them
  slightly(Hoffman et al. 1994)

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Ultimatum offers of children who failed/passed
false belief test
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Subject (autistic?) complaining post-experiment
(Zamir, 2000)
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Feeling This is your brain on unfairness(Sanfey
et al, Sci 13 March 03)
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Limited equilibrationBeauty contest game

• N players choose numbers xi in 0,100
• Compute target (2/3)(? xi /N)
• Closest to target wins 20

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Beauty Contest

• Some number of players try to guess a number that
  is 2/3 of the average guess.
• The answer cant be between 68 and 100 - no use
  guessing in that interval. It is dominated.
• But if no one guesses in that interval, the
  answer wont be greater than 44.
• But if no one guesses more than 44, the answer
  wont be greater than 29
• Everyone should guess 0! And good game theorists
  would
• But theyd lose

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Iterated Dominance

• People dont instantly compute all the way to 0
• The median subject uses 1 or 2 rounds of
  iteration (25, 35)
• Guessing 0 on the first round (game theorist) is
  poor
• Guessing 30 (behavioral game theory) is much
  better
• But 30 isnt a good guess the seventh time you
  play

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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 dont only care about their own
  payoffs?

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A New Theory of Utility

• Consider that people still like their payoffs
• They also dislike others having more money, with
  some coefficient ?.
• And they dislike having more money than others,
  with coefficient ?.
• U_1 is player 1s utility P_1 P_2 are the
  players payoffs.
• U_1 P_1 - ?(maxP_2 - P_1, 0) - ?(maxP_1 -
  P_2,0)
• ? is envy
• ? is guilt
• 0 lt ? lt 1 ? lt ?
• Different players can have different ? and ?

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Inequality Aversion

• U_1 P_1 - ?_1(maxP_2 - P_1, 0) -
  ?_1(maxP_1 - P_2,0)
• (Fehr and Schmidt 1999)
• Now, we can do classical game theory, but with U,
  not P
• Player 2 should reject any offer lt ?_2/(1 2?_2)
• If ? 1/3, player 2 should reject any offer less
  than 20
• Player 1 offers will depend on
• Estimates of player 2 envy (?_2) distribution
• and Player 1 guilt (?_1)

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Inequality Aversion Advantages

• Model generalizes easily to more than 2 players
• ? 1/3, ? 0 can explain a lot!
• Ultimatum bargaining
• Multi-player ultimatum bargaining (Market game)
• Even dictator games
• Parameters can be tuned for cultures or
  individuals
• Does not break most of the existing, correct
  predictions of non-IA game theory

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Inequality Aversion on Graphs

• For games where IA game theory works, we could
  put these games on graphs.
• Do players care about global inequalities or
  neighborhood inequalities?
• Our guesses may agree, but its an open question
  no experiment has been done!