agent-based modeling of cooperation in collective action situations & diffusion of information...
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Agent-based modeling of cooperation in collective action
situations & diffusion of informationMarco Janssen
School of Human Evolution and Social Change&
Department of Computer Science and Engineering
Arizona State University
Games and GossipMarco Janssen
School of Human Evolution and Social Change&
Department of Computer Science and Engineering
Arizona State University
Games and Gossip
• Games: Strategic interactions
• Gossip: Diffusion of information
Agent-based modeling is a way to study the interactions of large numbers of agents and the macro-level consequences of these interactions.
Organizations of agents
Animate agents
Data
Artificial world
Observer
Inanimate agents
If <cond>
then <action1>
else <action2>
If <cond>
then <action1>
else <action2>
…..
…..
….
Content
• Games– Why do we cooperate with strangers?– Changing the rules of the game
• Gossip– Diffusion of consumer products
Why do strangers cooperate?
• Dilemma between individual and group interests– Group interest: cooperation– Individual interest: free riding on efforts of others
• Public goods and common pool resources• Expectation with rational selfish agents
– No public goods– Overharvesting of common pool resources
• Many empirical examples of self-governance
The problem of cooperation in commons dilemmas
The puzzle of eBay
• Net revenues $2.2 billion for 2003.• In eBay strangers cooperate in non-repeated interactions of
traditional dilemma of buyer and seller.• Reputation system is found to be theoretically problematic
(aggregation, unlimited memory, entry problem)• Monitoring is incomplete
– About 55% of transactions include feedback.– About 1% of this feedback is negative.
• 90% of fraud on internet occurs in auction markets.• Puzzle: Why does eBay work?
eBay reputation system
• Buyer and Seller can provide “Feedback”: • Ratings translated into points: positive = 1
point, neutral = 0 points, and negative = -1 point. Aggregate is the reputation score.
• If reputation score reaches -4 the participant is removed from the system.
Simple model on reputation and trustworthiness
• Agents play one-shot prisoner dilemma games.• Reputation scores evaluates past behavior of the
actors.• Are reputation scores alone sufficient to derive
cooperation?• Especially, when not everybody provides feedback.• They may refuse to play and decide to cooperate or
not, based on expected trustworthiness.
Monetary payoff table of the Prisoner’s Dilemma with the option to withdraw from the game.
Player B
Cooperate Defect Withdraw
PlayerA
Cooperate 1,1 -2,2 0,0
Defect 2,-2 -1,-1 0,0
Withdraw 0,0 0,0 0,0
• Experiments have shown that the subjective evaluation of monetary payoffs lead to a different order of preferred situations than monetary rewards.
• Thus, utility and monetary rewards may differ.
Utility table of the Prisoner’s Dilemma with the option towithdraw from the game.
Player B
Cooperate Defect Withdraw
PlayerA
Cooperate 1,1 -2+βA, 2-αB
0,0
Defect 2-αA,-2+βB
-1,-1 0,0
Withdraw 0,0 0,0 0,0
α and β are individual characteristics of agents
How to estimate trustiness?
• The probability to trust the opponent:
• Where
• Adjusting weightings of symbols:
MeTr
1
1]Pr[
s
iii xwwM
10
Learning rate
Symbol i
Feedback (0 or 1)
,])Pr[( ii xTrFw
When to Cooperate?
• Estimate expected utilities:
Make discrete choice decision:
)]([)]([
)]([
][DUECUE
CUE
ee
eCP
)(])Pr[1(]Pr[)]([ iSTrRTrCUE
PTrTTrDUE i ])Pr[1()(]Pr[)]([
Population dynamics
• Agent remove from the system if they do not derive positive income, or when reputation score falls to -4.
• Agent is replaced with a random new one.
• Agents provide feedback with a certain probability.
Role of feedback(history 100 interactions)
0
0.2
0.4
0.6
0.8 1
0
0.3
0.6
0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
average payoff
probability feedback "positive"
probability feedback "negative"
0.9-1
0.8-0.9
0.7-0.8
0.6-0.7
0.5-0.6
0.4-0.5
0.3-0.4
0.2-0.3
0.1-0.2
0-0.1
Role of symbols
0
0.2
0.4
0.6
0.8 1
0
0.3
0.6
0.9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
average payoff
probability feedback "positive"
probability feedback "negative"
0.9-1
0.8-0.9
0.7-0.8
0.6-0.7
0.5-0.6
0.4-0.5
0.3-0.4
0.2-0.3
0.1-0.2
0-0.1
Finding
• Reputation systems with voluntary feedback might not be sufficient to foster cooperation.
• Observed high levels of cooperation might be explained by the use of multiple other sources of indicators of trustworthiness.
Changing the rules of the game
• Earlier work has focused on behavior of individuals and groups given a particular rule set, and what happens when this rule set changes.
• I am interested in how people change the rule of the game.
Questions on rule change
• How do individuals and groups know the potential effect of a rule change?
• What affect that persons invest in a rule change?
• What is the role of experience in rule crafting?
Using different type of methods
http://www.public.asu.edu/~majansse/dor/nsfhsd.htmDynamics of Rules project:
Laboratory Experiment
-Renewable resource-Collection of green tokens- 5 subjects: self is yellow dot; and other subjects are blue dots- move yellow dot around by arrow keys
Design
• For each treatment, a practice round and then 3 rounds of about 5 minutes.• Treatments:
– no rules – vote for rule (cost 50 tokens) – no rule (22 groups, 2 groups discarded)
– No rules for three rounds (4 groups, need more done later)– Rule imposed in 2nd round (9 groups)
• Totally 174 different subjects used (one person did an experiment twice)• In communication experiment we asked 30 persons to do it a second time.
Information collected
• Everytime a subject collect a token, the time, and place are recorded.
• Every 2 seconds the location of all tokens is recorded.
• When subjects break the rule and/or are caught (place and time)
• Questionaire at end of experiment.
What happens?
Round 1
0
50
100
150
200
250
300
350
400
450
500
2 32 62 92 122 152 182 212 242seconds
reso
urc
e s
ize
no rule
imposed
YES
NO
Effect of experience
0
50
100
150
200
250
300
350
400
450
500
2 32 62 92 122 152 182 212 242seconds
reso
urce
siz
e
no rule
imposed
YES
NO
experienced
Small but significant high collection of tokens and length of time
Round 2
0
50
100
150
200
250
300
350
400
450
500
2 32 62 92 122 152 182 212 242 272 302seconds
reso
urce
siz
e
Round 1
no rule
imposed
YES
NO
How much tokens collected? (including penalties)
0
200
400
600
800
1000
1200
1400
1600
no rule imposed yes notreatment
toke
ns c
olle
cted
in r
ound
1
2
3
How fast do they destroy the resource?
0
50
100
150
200
250
300
350
no rules imposed yes no
treatment
seco
nd
s re
sou
rce
exi
st
1
2
3
Average collected earnings of individuals
0
50
100
150
200
250
300
350
voted no (no) voted no(yes)
votes yes(no)
votes yes(yes)
1
2
3
Where did they break the rules?
0
100
200
300
400
500
600
700
1 4 7 10 13 16 19cells away from property
toke
ns
sto
len
Individual collected tokens in round 2 and 3
0
100
200
300
400
500
600
0 100 200 300 400 500 600
round 2
rou
nd
3
0
100
200
300
400
500
600
0 100 200 300 400 500 600
round 2
rou
nd
3
Not elected
Elected
0
100
200
300
400
500
600
0 100 200 300 400 500 600
round 2
roun
d 3
Imposed
0
100
200
300
400
500
600
0 100 200 300 400 500 600
round 2
rou
nd
3
No rule
CommunicationExperiment for designing future experiments
• Treatment 1: All three groups could communicate within one big group
• Treatment 2: The three groups split up and could talk among themselves.
• Experienced subjects!!
Global CommunicationAgreed Rule: 20 seconds wait, 10 seconds “go
for it”
0
100
200
300
400
500
600
700
800
2 32 62 92 122 152 182 212 242 272 302
seconds
reso
urc
e s
ize
123123123
Group talk:Areas of harvest
0
100
200
300
400
500
600
700
800
2 32 62 92 122 152 182 212 242 272 302
seconds
reso
urc
e s
ize
1
2
3
1
2
3
1
2
3
Next steps
• Analysis of data
• Development of agent-based models
• New experimental designs
Fun project• Why do recreational games have the rules they
have?
• Co-evolution of agents playing games and changing the rules such that certain objectives are derived (excitement of playing?).
EvaluationAgentsPlayGames(Tournament)
Adjustment of rules
Rules of tournaments
Diffusion dynamics in various types of social networks with heterogeneous consumers
with Alessio Delre & Wander Jager (University of Groningen, the Netherlands)
- How do network structure affect diffusion of consumer products?
- How do behavioral rules of consumer behavior affect diffusion processes? (Most models assume diffusion is a kind of epidemic spreading of a disease, we use cognitive theories)
Regular network (randomness = 0)
Random network (randomness = 1)
Small-World network (0 < randomness < 1)
Watts, D.J. and Strogatz S. H. (1998). Collective Dynamics of “Small-World” Networks, Nature, 393, 440-442.
Small-World Networks
Our innovation diffusion model
iiiiij yxU )1(
ii Afx )( , jii qpfy
1
0
otherwise
hAx
iii
0
1
otherwise
qpy
jii
Individual part:Social part:
where Ai is the number of adopters in set of neighbors of agent i
hi is a personal threshold which determines when agent i adopts.
)( ,,, MINijiji UUPa
P.S. Notice that we included mass media effects. Independently on word-of mouth process, at each time step, agents adopt with probability e.
Results -the speed of diffusion-ßi =1;
hi=0.3;
T
t
T
t
tf
tD
T
0
0
)(
)(1
D(t) = cumulative number of adopters;
f(t) = adopters at time t
0.3
0.4
0.5
0.6
0.7
0.8
0.0001 0.001 0.01 0.1 1
r
rho
Results -the speed of diffusion in heterogeneous populations-
0.4
0.5
0.6
0.7
0.8
0.9
1
0.04 0.06 0.08 0.1 0.12 0.14 0.16
std dev
rho
Continuous line: <hi>=0.4;
Dashed line: <hi>=0.3;
Pointed line: <hi>=0.2.
Application: hits and flops of movies
• What makes a movie a hit? Spread of information?• Most movies have their most successful week in the
first week.• Only in rare cases there is an increase after the first
week.• Same phenomena with best seller books (Harry
Potter).• Expectations are formed by media campaign before
the product is available.• Survey data from movie-goers (challenging
fieldwork!!)
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