Transcript Cultural Emergence in Game Ensembles: An Experimental Study

The Emergence of Cultural Signatures and
Persistence of Internal Diversity:
A Model of Conformity and Consistency
Jenna Bednar
Aaron Bramson
Andrea Jones-Rooy
Scott E Page
Outline
• Background
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Culture
Institutions and Mechanism Design
Ensembles of Institutions
Broad Forces: Coordination & Consistency
• Coordination Consistency Model
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Coordination Model
Our Model
Analytic Results ( and 2)
Computational Results (the rest)
Culture?
Behavior
Beliefs
Semiotics
Preferences
Norms
Survey Approach
Hoftstede:
Power Distance
Individualism
Masculinity
Uncertainty Avoidance
US
Power Distance
Individualism
Masculinity
Uncertainty Avoidance
32
90
60
40
France
Power Distance
Individualism
Masculinity
Uncertainty Avoidance
61
63
32
80
El Salvador vs Korea
Power Distance
Individualism
Masculinity
Uncertainty Avoid
El Sal
62
12
41
80
Korea
56
11
33
80
Institutions and Behavioral
Repertoires
Larger Project
Behavioral
Repertoire
Institutions
Bednar and Page (2007) “Can Game(s) Theory Explain Culture? The
Emergence of Cultural Behavior Within Multiple Game” Rationality and
Society
Larger Project
Behavioral
Repertoire
Institutions
Bednar and Page (2007) “Can Game(s) Theory Explain Culture? The
Emergence of Cultural Behavior Within Multiple Game” Rationality and
Society
Mount-Reiter Diagram
Social Objective
Environment
Outcome
Behavioral
Rule
Outcome
Function
Actions
(Message Space)
Equilibrium requires COORDINATED behavior:
- tit for tat
- costly signaling
- alternation
- driving on the left
Multiple Institutions
E
O
E
M
E
M
O
M
O
E
O
M
Bednar (2008), Bednar and Page (2007)
Empirical evidence suggests that people
avoid cognitive dissonance, that they
used cased based decision rules, and
that they transfer routines from one
setting to another.
We call this consistency.
Coordination Consistency
Model
Pure Coordination Game
Player 2
Player 1
A
B
A
B
1,1
0,0
0,0
1,1
Hard and Soft Externalities
An externality is hard (economic) f it’s
easily measured
An externality is soft (psychological) if it’s
not.
No Bright Line
Some decisions involve both hard and
soft coordination externalities.
Suppose I’m buying a bike. The more
people that buy mountain bikes, the
more trails that get created (hard).
Buying a mountain bike might also
make me hip (soft).
Two empirical regularities explained and
two inconvenient truths that lie outside
the model.
Coordination
Exception Proves Rule
Qui ckTi me™ and a
TIFF (Uncompressed) decompressor
are needed to see this pictur e.
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Dagen H
At 4:45 am on September 3, 1967, all
cars on the road in Sweden came to a
stop. They switched sides (from the left
to the right) and at 5 am, the cars began
moving again.
ICT1: Diversity within Cultures
ICT2: Cultural Signatures
Elevator Version
Describe a model in which agents attempt to coordinate
with others and to be internally consistent that
produces intra cultural heterogeneity, inter cultural
heterogeneity, and cultural signatures.
A List of Questions
Ketchup in the fridge?
Do people wear shoes inside your house?
Do you cross the street when the don’t walk sign is
flashing?
Read the newspaper at the breakfast table?
Do you hug your friends when you see them?
Paper napkins?
YNYYY Nation
Ketchup in the fridge? Yes
Do people wear shoes inside your house? No
Do you cross the street when the don’t walk sign is
flashing? Yes
Read the newspaper at the breakfast table? Yes
Do you hug your friends when you see them? Yes
Paper Napkins? Yes
How Many Cultures?
Six questions
Two answers each
2 x 2 x 2 x 2 x 2 x 2 = 64
The Set of The Possible
Dead People: bury or burn
Foods you eat?
Dress?
Music you play
Stories you tell
8 x 19 x 40 x 6 x 11 x 23 x 2 x 43 .. = HUGE
Four Assumptions
Coordination: incentive to choose an
equilibrium action
Consistency: incentive to be consistent across
games
Dynamics: people learn
Errors: people make mistakes
Model
Agent: (H,C,C,H,H,C,C,C)
Coordination rule: match actions of others in
common games
Consistency rule: match actions of self on
different games
Coordination Rule
Pick two players at random and a game at
random. Set the action of the first player
equal to the action in the second player.
(H,C,C,H,H,C,C,C) meets (C,H,C,C,H,C,C,H)
(C,C,C,H,H,C,C,C)
Coordination Equilibrium
All agents should coordinate in each game but
the choices of actions should be arbitrary.
Distinct cultures but no signatures.
(C,C,C,H,H,C,C,C)
Consistency Rule
Pick two games at random. Set the action in
the first equal to the action in the second.
(H,C,C,H,H,C,C,C)
(C,C,C,H,H,C,C,C)
Consistency Equilibrium
Each agent should be consistent but no two
agents need be consistent in the same way.
Consistent people but no coordination.
(C,C,C,C,C,C,C,C)
(H,H,H,H,H,H,H,H)
Coordination & Consistency
With probability p an agent applies the
coordination rule, and with probability
(1-p) an agent applies the consistency
rule.
Equilibrium
Societies converge to either
(C,C,C,C,C,C,C,C) or (H,H,H,H,H,H,H,H)
Two Considerations
The Second Law
The Trembling Hand
The Second Law
The second law of thermodynamics
suggests a unique stable equilibrium--but it’s not of much predictive value.
Simplest Model
Two agents
Two games
Two actions
States of the World
Coordinated and Consistent
Off by One
Consistent not Coordinated
Coordinated not Consistent
Neither (Total Mess)
Consistency Dynamic
1
2
1
2
2
1
Consistency Transition Map
1
1/4
1/2
1/4
1
Coordination Transition Map
1
1/4
1/2
1
1/4
Coordination & Consistency
Transition Map
1/2
1
1/4
1/8
1/2
1/8
1/2
1/2
1/2
Time To Convergence
p = probability of coordination
Limiting Case
With N agents and M dimensions time to equilibrium
scales as follows:
T ~  N2M2
for p near 1/2
T ~  N2M/p
for p near 0
T ~  M2N/(1-p) for p near 1
Scott E Page, Leonard M. Sander, and Casey Schneider - Mizell
``Conformity and Dissonance in Generalized Voter Models” Journal of
Statistical Physics, 2007.
The Trembling Hand
Agents make mistakes with probability
epsilon.
Markov Process
1- 

0
1/4 (1- )/2 .
0
..
0
Equilibrium
Tremble of size  leads to 2 deviation
from consistency and coordination in
the single force models but at least 6
deviation in the model with both forces.
Proportion of Population not at
Pure Strategy Equilibrium
 = amount of tremble (error)
100 Agents, 10 Games, 5 Actions
Heterogeneity and Cultural Signatures
Summary
• Model Produces
– Inter cultural differences
– Intra cultural differences
– Cultural signatures
• Methodological Insights
– Models can be too simple
– Ensembles of games different from games
Summary
Future Directions
– Institutional choices induce behavior
– Those behaviors can create spillovers
Other Applications
– Party members’ ideal points
– Organizational culture