Behavioral Game Theory:
A Brief Introduction
Networked Life
CSE 112
Spring 2005
Prof. Michael Kearns
Supplementary slides courtesy of Colin Camerer, CalTech
Behavioral Game Theory
and 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
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 x>0
Empirical:
Reject x=$2 half the time
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:
1.
2.
Player 1 offers close to, but less than, half (40% or so)
Player 2 rejects low offers (20% or less)
Ultimatum offer experimental sites
Ultimatum Bargaining across Cultures
Sharing norms differ in the industrialized world
Japan, Israel lowest (Roth et al. 1991)
Machiguenga farmers in Peru (Henrich 2000)
Offered 26% on average, accepted all but 1 offer
Very socially disconnected
Ache in Paraguay, Lamelara in Indonesia
Made hyperfair (more than 50%) offers
Headhunters (potlatch culture), whalers
The Machiguenga
independent families
cash cropping
slash & burn
gathered foods
fishing
hunting
Fair offers correlate with market integration (top),
cooperativeness in everyday life (bottom)
Ultimatum offers across societies
(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 Looks
70 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 difference
Woman as player 1, attractive man as player 2…
Average offer is 50.7% (hyperfair!)
Small percentage (1 or 2?) offer almost everything
Stakes, Entitlement, Framing
Indonesia: from a day’s wages to a month’s 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)
Ultimatum offers of children who
failed/passed false belief test
Subject (autistic?) complaining postexperiment (Zamir, 2000)
Feeling: This is your brain on unfairness
(Sanfey et al, Sci 13 March ’03)
1. Limited equilibration
Beauty contest game

N players choose numbers xi in [0,100]

Compute target (2/3)*( xi /N)

Closest to target wins $20
relative
frequencies
Beauty contest results (Expansion,
Financial Times, Spektrum)
average 23.07
0.20
0.15
0.10
0.05
0.00
numbers
22
100
50
33
num be r choice s
97
89
81
73
65
57
49
41
33
25
17
9
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
1
predicted frequency
0
Beauty Contest
Some 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 Dominance
People don’t 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 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 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 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 Aversion
U_1 = P_1 - _1(max[P_2 - P_1, 0]) - _1(max[P_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 < _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)
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
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 it’s an open
question: no experiment has been done!