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Defining Collective Action
Collective-action problem: Individual decision-making leads to socially undesirable (Pareto-inefficient) outcomes
Cooperation: Adjusting behavior to minimize socially undesirable outcomes
Tragedy of the Commons
Garrett Hardin (1968):“Therein is the tragedy. Each man is locked into a system that compels
him to increase his herd without limit—in a world that is limited. Ruin is the destination towards which all men rush, each his own best interest in a society that believes in freedom of the commons.”
“Mutual coercion, mutually agreed upon”
Flip side of resource use: Maintenance of ecosystems/public goods
Collective action problems are ubiquitous!
Studying Collective Action
Major Research Questions
1. Factors explaining cooperative behavior
2. Role of institutions (e.g., punish defection, reward cooperation)
Theoretical Philosophy Game theory Evolutionary game theory Evolutionary simulations (This talk)
Empirical Field research (qualitative and quantitative) Experimental research
Prisoner’s DilemmaPlayer 2
Cooperate Defect
Player 1
Cooperate R1= 6
R2= 6
S1= 3
T2= 8
Defect T1= 8
S2= 3
P1= 4
P2= 4
Conditions: T>R>P>S; 2R>T+S
Nash equilibrium: Both players defect
Collective Action Agents
Five “gene” strategies; 32 possible Each gene determines behavior in current
round on basis of outcome in last round
<Nice (1st round), Reciprocal (CC), Sucker(CD), Forgive (DC), Protect (DD)>
Important Examples:All Cooperate <1,1,1,1,1>
GRIM Trigger <1,1,0,0,0>
PAVLOV(Win-stay, lose shift) <1,1,0,0,1>
Tit-for-Tat <1,1,0,1,0>
Structure of Simulation
Generation 1 Generation 5000
Generation 1: Randomly Select 40 Strategies
Round Robin Tournament: Each strategy vs. itself and all others
Proportional Fitness Reproduction:
P(reproduction)= Fitnessi/Fitnessall
Next Generation:
Survival of Fittest
1% Mutation Rate on Each Gene
A “Punishing” Experiment
Design Baseline 2-player repeated PD, with discount
rate= .9 Examine the effect of $2 punishment for defection,
with increasing probability ranging from [0,1] in .10 increments
10 runs of each experiment; 40 strategies, 5000 generations
Hypotheses Increasing levels of cooperation Increased population stability Shift in the population dynamics of cooperation
0
1
2
3
4
5
6
7
MeanFitness
0
5
10
15
20
25
30
35
40
45
1
29
0
57
9
86
8
11
57
14
46
17
35
20
24
23
13
26
02
28
91
31
80
34
69
37
58
40
47
43
36
46
25
49
14
grimpavlov
Bas
elin
e:
No
Pu
nis
hm
ent
Ho
bb
es:
Pu
nis
hm
ent
p=
1.0
0
1
2
3
4
5
6
7
MeanFitness
0
5
10
15
20
25
30
35
40
45
1
295
589
883
1177
1471
1765
2059
2353
2647
2941
3235
3529
3823
4117
4411
4705
4999
grimpavlov
4.4
4.6
4.8
5
5.2
5.4
5.6
5.8
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Punishment Probability
Mea
n F
itn
ess
Generation MeanFitness
Mean Fitness Increases With Punishment Probability
0
5
10
15
20
25
30
35
40
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Punishment Probability
Av
era
ge
Ge
ne
Fre
qu
en
cy
Pe
r G
en
era
tio
nNice CC CD DC DD
Gene Frequency: All Regimes
Strategy Frequency: All Regimes
0
2
4
6
8
10
12
14
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Punishment Probability
Ave
rag
e S
trat
egy
Fre
qu
ency
GRIM
PAVLOV
SPAVLOV
Gene Frequency: Cooperative Regimes (Avg. Fitness>5.9)
0
5
10
15
20
25
30
35
40
45
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Punishment Probability
Gen
e F
req
uen
cy
Nice CC CD DC DD
Strategy Frequency: Cooperative Regimes
-1
4
9
14
19
24
29
34
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Punishment Probability
Ave
rag
e S
trat
egy
Fre
qu
ency
GRIM
PAVLOV
SPAVLOV
TFT
Some Correlations
Overall Fitness .21
Genes
Nice .11
CC .22
CD .10
DC .06
DD .24
Strategies
All Defect -.18
GRIM -.03
PAVLOV .10
Suspicious PAVLOV .10
TFT .04
Conclusions
Punishment institutions increase cooperation and stability, even in noisy environment
As punishment increase, basis of cooperation shifts towards PAVLOV
Institutions change population dynamics of cooperation, even if same behaviors observed
Must square with observed human behavior; e.g.; resistance to coercion, reduced effectiveness of reciprocity in coercive environments