Exit for Cooperation
--A Simulation Study-Yuhsuke Koyama (Tokyo Tech)
Hirokuni Ooura (Teikyo)
Jun Kobayashi (Chicago)
August 15, 2004
ASA, San Francisco
OVERVIEW
Free-riding and Mobility?
Simulation, Agent-Based
EVOLUTION of Cooperation
MATCHING among Strategies
QUESTION
Modern Societies... MOBILITY
Turnover, Divorce, Moving,
Immigration
Globalization, Internet
Effects of MOBILITY
on FREE-RIDER PROBLEM?
EVOLUTION of Cooperation???
3
FREE-RIDER PROBLEM
When Goods have Externality
Promise, Donation
Teamwork, Social Movement
RATIONAL to FREE-RIDE
but EFFICIENT to COOPERATE
4
OUT-FOR-TAT (Hayashi)
Simulation, 2-person game
“EXITING” is Effective as Revenge
if Mobility Cost is HIGH
Free-rider
Cooperator
MULTIPLE-PERSON Games?
Introduction
Method
Result
SIMULATION
AGENT-BASED, JAVA
SHARE Change of 4 Strategies
MOVING TFT (MT)
Cooperator
FIXED TFT (FT)
MOVING ALL D (MD)
FIXED ALL D (FD)
(Move to Most Profitable, Largest)
Cooperators can REJECT???
GAME
100 Agents
Each with 1 of 4 Strategies
Randomly Assigned to 10 Groups
Free-rider Problem x 5 rounds
-> Exit Option
Free-rider Problem x 5 rounds 100
-> Exit Option
(repeated till 20 Exit Options)
A
B
... J
Free-rider
Problem
Exit
Option
FREE-RIDER PROBLEM
Resource $4
PROVIDE or NOT
Pooled Resources DOUBLED
EQUALLY Distributed in Group
# Providers
u (Provide) = 8
Group Size
#
Providers
-1
u (Not) =
8
+4
Group Size
EVOLUTION
SHARE CHANGE after Game
Proportional to PAYOFF x SHARE
Mobility Cost = $1
Repeat 100 Games
3 Possible OUTCOMES
ALL Cooperators
ALL Defectors
Draw (Otherwise)
WINS and LOSSES
# Strategies = Multiples of 5
All Initial Distributions = 1,771
30 Iterations for Each Distribution
“WIN” if Cooperators Dominate 21
“LOSS” if 10 Iterations
(H0: Even, p<.05, Two-sided Test)
FOCUS
Defectors Reject Cooperators
Many Cooperators+Few Defectors
Fixed Defector
Moving
TFT
Fixed
TFT
Moving Defector
Initial Distributions -> WINS???
Introduction
Method
Result
0 and 5 FIXED DEFECTORS
Fixed Defector
MD
MT
FT
Moving Defector
MD
LOSS
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
0
30
30
30
30
30
30
30
30
30
30
29
28
19
20
16
11
4
4
1
0
0
5
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
10
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
0
30
30
30
30
30
30
29
22
16
14
11
4
4
0
0
0
15
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
5
30
30
30
30
30
30
25
20
23
15
14
17
18
13
15
12
20
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
10
30
30
30
30
30
29
23
26
25
20
19
16
13
15
14
8
25
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
15
30
30
30
30
30
27
27
25
20
19
20
20
16
22
13
17
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
20
30
30
30
28
30
29
26
25
26
23
19
17
18
16
19
15
35
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
25
30
30
30
29
30
30
23
24
25
23
23
21
19
20
20
19
40
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
28
30
29
29
25
23
24
18
22
23
19
45
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
35
30
30
30
30
30
30
29
30
25
26
24
25
22
27
25
22
40
30
30
30
29
30
30
30
28
29
27
27
27
28
26
26
21
FT
50
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
FT
45 50
30 30
30 30
30 30
30 30
30 30
29 29
30 29
28 30
27 30
27 29
27 29
27 30
27 30
28 26
29 26
27 29
55
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
60
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
55
30
30
30
30
30
30
30
29
30
26
28
30
27
28
28
28
65
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
60
30
30
30
30
30
30
28
29
29
29
28
28
28
30
29
29
70
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
65
30
30
30
30
30
30
29
29
28
29
28
30
30
26
30
29
75
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
70
30
30
30
30
30
29
30
28
29
30
30
27
29
30
30
29
80
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
75
30
30
30
30
30
30
30
30
30
30
30
29
26
29
29
30
85
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
30
80
30
30
30
30
30
30
29
30
30
30
30
29
30
30
30
29
90
30
30
30
30
30
30
30
30
30
30
30
85
30
30
30
30
30
30
30
29
30
30
30
90 95
30 30
30
30
30
30
30
95 100
30 30
30
30
30
30
30
WIN
10, 15, 20 FIXED DEFECTORS
MD 0 24 25 24 21 24 27 23 20 24 26 25 19 15 15 10 10
Fixed Defector
MT
FT
Moving Defector
MD
0
1
2
3
4
5
6
7
8
9
10
0
30
27
27
23
19
10
7
5
1
0
0
0
1
MD 2
3
4
5
FT
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85
30 30 28 30 29 30 28 29 30 28 29 25 28 22 27 26 18 10
22 21 16 11 16 16 11 8 14 11 6 11 12 11 12 8 8
14 9 10 6 13 11 6 7 4 3 6 5 3 7 3 4 5
7 7 8 6 6 3 5 4 4 1 2 3 5 1 3 2 4
2 4 4 1 4 1 2 2 1 0 2 3 2 4 2 5 2
4 0 1 4 2 1 1 1 0 3 0 7 3 1 1 3 0
5
30
30
27
21
24
15
13
8
9
5
3
15
30
28
23
17
14
15
7
3
3
4
6
10
30
26
22
22
16
11
17
8
9
7
3
20
30
24
23
19
6
9
9
7
7
8
5
25
30
27
24
23
15
10
10
6
4
5
5
30
30
28
24
15
15
7
14
5
5
3
6
35
30
27
25
13
10
10
7
12
9
3
2
40
30
28
25
19
12
11
7
9
8
6
8
FT
45
30
29
18
18
11
13
9
9
7
9
7
50
30
24
23
20
10
12
11
13
9
9
12
55
30
27
20
20
14
11
13
9
14
9
15
60
30
26
25
19
16
15
15
13
12
11
16
65
30
27
25
12
14
17
11
17
11
14
16
70
30
28
20
19
17
16
17
18
17
12
18
75
28
27
17
16
16
20
22
21
16
18
20
80
30
25
23
21
15
16
16
16
17
18
16
85 90
30 27
28
25
25
18
18
4
1. EVOLUTION of COOPERAITON
Cooperators can REJECT (Blue)
If FEW Defectors
Even with MOBILITY
Up to about 15 Defectors
b/c 10 Groups
2. MATCHING
Cooperators Refuse TOGETHER
Fixed Defector
Moving
TFT
Fixed
TFT
Moving Defector
SUMMARY
1. Evolution of Cooperation
Even with Mobility
2. MATCHING matters
More STRATEGIES?
More MOBILITY COSTS?
Compare with Experiment, Survey