RISE and FALL of
COOPERATION
Jun Kobayashi (Seikei U)
Yuhsuke Koyama (Tokyo I of Tech)
Hideki Fujiyama (Dokkyo U)
Hirokuni Oura (Teikyo U)
August 15, 2005
ASA, Philadelphia
OVERVIEW
Mutual Effects of Group
Cooperation Rate & Group Size?
(traditional)
Social Dilemma Experiment w/
Intergroup Mobility
(Not traditional)
3
QUESTION
 Olson... Size↑→Cooperation↓
 Free-rider Problem, Social Dilemma
 Counter Effect?
 Modern Societies… Exit Option
 Moving, Job change, Divorce
 Effect of Group Cooperation Rate on
Group Size???
ON the RUN (Erhart + Keser)
 Experiment, Intergroup Mobility
 9 players in 3 group, 10 Sessions
 Cooperators RUN AWAY
 Cycle:
Size↑→Cooperation↓→ S↓→C↑
 Various Conditions???
Introduction
Data
Result
6
EXPERIMENT
 2003/4, 4 universities in Japan
 10 Sessions, 170 Students
 ¥1289.0 ($11), 90 minutes
 Computer-based, Group data
 “LOW” “MIDDLE” “HIGH” Mobility
 17 in 4 Groups, Anonymous
 10 Rounds, 9 Exit chances
7
8
ROUND (10 times)
A
B
C
D
Free-rider
Problem
Exit
Chance
9
1. FREE-RIDER PROBLEM
Resource ¥20
PROVIDE or NOT
Pooled Resources...
DOUBLED...3/more-player groups
x 1.5...
2-player Groups
SAME...
1-player Groups
EQUALLY Distributed in Group
10
EXAMPLE (4 Players)
x2=
Provide
Not
Not
Not
Provide = 40m/4 = 10m
(Providers)
Not = 40(m-1)/4 + 20 = 10m + 10
11
2. EXIT CHANCE
LOW Mobility... ¥50 to Exit
MIDDLE Mobility... ¥20
HIGH Mobility... ¥0
Groups’ Average Payoffs
Last Stage
Group C Round 2 Stage 2
Your Decisions and Payoffs in This Round
A
33.33
B
25.00
C
27.50
D
25.00
Stage
Your Decision
Your Payoff
1
NOT
35.00
2
PROVIDE
5.00
Groups’ Average Payoffs
in This Round
A
33.33
B
25.00
Your Total: 125 yens
C
27.50
(20 yens subtracted for Moving)
D
25.00
Groups’ Size
A
3
B
4
C
8
D
2
Group C's Members: You (ID 6) and Other 7
What do you do next stage?
PROVIDE 20 yens
NOT
Provided 20 yens: 3 persons
Not:
4 persons
Your Decision:
Provide
Your Payoff:
17.14 yens
Groups’ Average Payoffs
and Size last Round
A
30.00
3
B
33.33
4
C
25.00
8
D
27.50
2
ROUND END
Groups’ Average Payoffs
Group
Stage 1
2
3
4
5
A
33.33
20.00
15.55
24.76
35.00
B
25.00
35.00
19.10
35.00
35.00
C
27.50
27.50
22.00
27.50
20.00
D
25.00
35.00
25.00
25.00
18.88
Your payoff Last Round: 112 yens in Group C
Which Group in Next Round? Move with
Group A
B
C
D
50 yens
HYPOTHESES
 H1. Size↑→Cooperation↓
Cooperation
Rate
 H2. Cooperation↓→ Size↓
H2
H1
H1
H2
Size
 H3. Mobility↑→Cycle Accelerated
REGRESSION ANALYSES
 Unit… Group (N=360)
 H1. Size↑
Cooperation↓
Round Number, Previous Cooperation
 H2. Previous Coop.↓
Size↓
Round Number, Previous Size
Introduction
Data
Result
18
DESCRIPTIVE STAT.
Cooperation Rate
¥50
0.500
0.400
0.300
0.200
0.100
0.000
0.000
0.200
¥20
¥0
0.400
Mobility Rate
0.600
0.800
H1. SIZE on COOPERATION
Cooperation Rate
¥50
¥20
¥0
0.8
0.6
0.4
0.2
0
1 2 3 4 5 6 7 8 9 10 11 12
Size
y = COOPERATION RATE
Mobility Cost
¥50
¥20
¥0
ROUND
.00
.00
.00
SIZE
-.04*** -.05*** -.03*
Previous COOP. .47*** .11
-.04
R2
.32
.16
.11
＊p<.05, ＊＊.01, ＊＊＊.001
H2. COOPERATION on SIZE
Size
¥50
¥20
10
8
6
4
2
0
¥0
10
8
6
4
2
0
0
1
10
8
6
4
2
0
0
1
0
Previous Cooperation Rate
1
y = SIZE
Mobility Cost
¥50
¥20
¥0
ROUND
.00
-.01
.07
Previous COOP. 2.12*** 3.11*** 4.83***
Previous Size .83*** .65*** .36**
R2
.60
.37
.27
＊p<.05, ＊＊.01, ＊＊＊.001
H3. MOBILITY on CYCLE
Cooperation
Rate
¥50
¥20
¥0
0.8
0.6
0.4
0.2
0
0
1
Size
¥50
¥20
¥0
Size
6
4
2
0
0
1
Previous Cooperation Rate
 Interaction Effects… Not Significant
EXAMPLES of CYCLE (LOW)
¥50
8
Cooperation
Group A B
C
D
0.8
6
0.6
4
0.4
0
Round
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
0.2
1
2
3
4
5
6
7
8
9
10
2
1
2
3
4
5
6
7
8
9
10
Size
1
Cooperation
Rate
Size
MIDDLE MOBILITY
¥20
Size
Cooperation
12
1
10
0.8
8
0.6
6
0.4
4
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
0
1
2
3
4
5
6
7
8
9
10
0.2
1
2
3
4
5
6
7
8
9
10
2
HIGH MOBILITY
¥0
Size
Cooperation
14
12
10
8
6
4
2
0
1
0.8
0.6
0.4
0.2
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
0
28
SUMMARY
 Large Groups DECREASE
Cooperation, then SHRINK
 Then INCREASE Cooperation, then
EXPAND
 MOBILITY ACCELERATES Cycle