Transcript Game Theory and Economics

University of Auckland
Winter Week Lectures
Third Lecture
4 July 2007
Associate Professor
Ananish Chaudhuri
Department of Economics
University of Auckland
1
What affects beliefs and
cooperation?
• Mark Isaac and James Walker look at
• Group size
• What happens when the size of the group
changes (small or large)
• Collective action may be more difficult with
larger groups
• Marginal Per capita return (MPCR)
• What happens when the return on the
investment goes up or goes down?
• With 4 players if each dollar contributed is
DOUBLED and redistributed equally then the
return per dollar is (2/4) = $0.50. If $1 is TRIPLED
and divided by 4 then the return is (3/4) = $0.75
What affects beliefs and
cooperation?
• Amount placed in the private
account for each player is known
only by that particular player
• Everyone knows the total
contribution to the group account
• Play for 10 periods
• Players are told their total earnings
at the end of each round
3
What affects beliefs and
cooperation?
4
5
Results
Average contributions in percent
6
Results
• Cooperation increases with MPCR
for both groups of size 4 and groups
of size 10.
• Cooperation increases with group
size if MPCR is low (not when it is
high).
• Cooperation decreases over time
7
What happens if we use
even larger groups?
• Isaac, Walker and Williams look
at groups of 4, 10, 40 and 100
• Two MPCR treatments:
• MPCR = 0.3
• MPCR = 0.75
8
LOW RETURNS
HIGH RETURNS
Larger groups do
better
Not much
difference
n = 40
n = 100
n = 10
n=4
9
What happens if we use
even larger groups?
• For MPCR = 0.3 larger groups
are more cooperative
• For MPCR = 0.75 no strong
difference but larger groups are
certainly not less cooperative
10
Would providing more
disaggregated information help?
• In many social dilemma experiments we
provide the participants information about
average contributions for the group
• What if we showed them contributions
made by individuals without revealing their
identity?
• Turns out the this increases free-riding!
11
12
Communication & Voluntary
Cooperation
• Groups of four
• Two sequences with 10 periods each
• Group composition remains
unchanged for the duration of the
session.
• Communication opportunities:
Players can discuss what they want
to do in the experiment.
13
Communication & Voluntary
Cooperation: Treatments
• 1. Communication for 10 periods followed
by No Communication for the next 10
periods (players have the same
endowment.)
• 2. No Communication for the first 10
periods followed by Communication in the
next 10 (players have the same
endowment)
• 3. Communication followed by No
Communication (asymmetric endowments).
14
15
Findings
• Start with Communication
• High cooperation rates; also in the
second No Communication phase.
• Start with No Communication
• Unraveling of cooperation in No
Communication but after Communication
rapid increase in cooperation.
16
Cooperation, Punishments
and Social Norms
• A social norm is
• a behavioral regularity that
rests on a common belief of
how one should behave
• and might be enforced by
formal or informal sanctions.
17
A cooperation and punishment
experiment
(Fehr and Gächter, 2000)
• Stage 1:
• typical public goods game
• Stage 2:
• Punishment opportunity
• Subjects are informed about each
member’s contribution.
• Subjects can punish other group
members at a cost to themselves.
18
A cooperation and
punishment experiment
• Either groups are fixed – “partners”
protocol
• Or players are randomly rematched at the end of each round –
“strangers” protocol
19
Predictions
• If players are selfish and
interested in maximizing their
earnings then:
• No punishment
• No contribution regardless of whether
there is a punishment opportunity.
20
Predictions
• Players in the partner treatment who
interact with the same people over
and over again may be able to build
up a group reputation
• “There are punishers in the group, hence
it is better to cooperate”
• Building such reputation would be difficult
with random re-matching where the
interactions are short-lived
21
22
(18.5%)
(57.5%)
(9.5%)
(61.5%)
23
Who gets punished?
24
Even non-monetary punishments
(scolding?) seem to matter!
• David Masclet and others look at a
“partners” treatment where participants
play for 30 periods divided into 3
segments
• No sanction (periods 1 through 10)
• Monetary Sanction OR Non-Monetary
Sanction (Periods 11 through 20)
• No sanction (Periods 21 through 30)
25
Group Contributions Over Time
Monetary
punishment
Non-monetary
punishment
26
Formal vs. Informal Sanctions
• The availability of either type of
sanctions increases contribution levels.
• The availability of non-monetary
sanctions initially increases the
contribution levels of subjects by as
much as monetary sanctions.
• The increase in contribution resulting
from non-monetary sanctions is not as
durable as the increase from monetary
sanctions.
27
How effective are non-monetary
punishments?
• Monetary punishment alone is a
blunt tool to raise contributions than
needed.
• A wider array of sanctions is more
effective.
• For many people, non-monetary
sanctions are sufficient to induce high
contributions.
• Costly monetary punishments can be
reserved for those that informal
sanctions cannot influence.
28
Are punishments essential?
Creating culture in the
laboratory
• A group of 5 subjects play the
public goods game for 10
periods.
• After her participation, each
agent is replaced by another,
who plays the game for 10
periods again.
29
The Inter-generational
paradigm
• Players in any generation can
leave free-form written advice
to their successors
• Players get two payoffs – what
they earn plus what their
progeny earn
30
Three Different Advice
Treatments
• In the private advice treatment
advice from generation “t”
player is given only to her
successor in generation “t+1”
• In the public advice almost
common knowledge treatment
advice from all players in
generation “t” is given to all the
players in generation “t+1”
31
Three Different Advice
Treatments
• In the public advice common
knowledge treatment advice
from all players in generation
“t” is given to all the players in
generation “t+1”and is also read
aloud by the experimenter
• The advice treatments are
compared to behavior in a
control group
32
The Inter-generational
Paradigm
• In real-life when we are confronted
with a social dilemma we often
access to the wisdom of the past in
the sense that predecessors, or at
least immediate predecessors, of
this person are available to give us
advice.
33
Pattern of Contributions
Common
Knowledge advice
4
6
8
Pooled Data
2
Private advice
0
No advice
0
2
4
6
8
10
Period
No Advice
Com mon Knowledge
Private Advice
Almost Com mon Knowledge
34
Evolution of Contributions Across
Generations – Private Advice
Private Know ledge Generation 1
18
16
14
12
10
Percentage
8
6
4
2
Private Knowledge Generation 1
0
0
1
2
3
4
Tokens
5
6
7
8
9
10
35
Evolution of Contributions Across
Generations – Private Advice
25
20
15
Private Knowledge Generation 2
Percentage
10
5
Private Knowledge Generation 1
0
0
1
2
3
4
Tokens
5
6
7
8
9
10
36
Evolution of Contributions Across
Generations – Private Advice
25
20
Private Knowledge Generation 3
15
Percentage
Private Knowledge Generation 2
10
5
Private Knowledge Generation 1
0
0
1
2
3
Tokens
4
5
6
7
8
9
10
37
Contributions Across Generations – Almost
Common Knowledge
Almost Common Know ledge Generation 1
30
25
20
Percentage 15
10
5
Almost Common Knowledge Generation
1
0
0
1
2
3
4
Tokens
5
6
7
8
9
10
38
Contributions Across Generations – Almost
Common Knowledge
30
25
20
Almost Common Knowledge Generation
2
Percentage 15
10
5
Almost Common Knowledge Generation
1
0
0
1
2
3
4
Tokens
5
6
7
8
9
10
39
Contributions Across Generations – Almost
Common Knowledge
70
60
Almost Common Knowledge Generation
3
50
Percentage
40
Almost Common Knowledge Generation
2
30
20
10
Almost Common Knowledge Generation
1
0
0
1
2
3
Tokens
4
5
6
7
8
9 10
40
Contributions Across Generations –
Common Knowledge
Common Know ledge Generation 1
18
16
14
12
Percentage
10
8
6
4
2
Common Knowledge Generation 1
0
0
1
2
3
4
Tokens
5
6
7
8
9
10
41
Contributions Across Generations –
Common Knowledge
50
45
40
35
30
Percentage 25
20
15
10
5
0
Common Knowledge Generation 2
Common Knowledge Generation 1
0
1
2
3
4
Tokens
5
6
7
8
9
10
42
Contributions Across Generations –
Common Knowledge
50
45
40
35
30
Percentage 25
20
15
10
5
0
Common Knowledge Generation 3
Common Knowledge Generation 2
Common Knowledge Generation 1
0
1
2
3
Tokens
4
5
6
7
8
9
10
43
Role of Advice
• Subjects were asked to indicate a
specific contribution in addition to
providing free-form advice
• Often, advice specified a dynamic
rule:
• “I would pick a high number for the first round
like 9. But when you see the average start to
drop, pick a small number so you don’t lose
money.”
44
Role of Advice
• In the later generations of common
knowledge public advice, subjects
advised unconditional contribution:
• “Keep faith! No one should mess it up for the
others. All 10 for all 10 rounds!”
• “For goodness’ sake don’t be that morally vacant
girl who prioritizes her own profit & takes
advantage of everyone else!”
45
Histogram of Advice Left – Private
Advice
Private Generation 1
30
25
20
Percentage 15
10
5
Private Generation 1
0
0
5
5.5
6
6.5
Advice Left
7
7.5
8
8.5
9
10
46
Histogram of Advice Left – Private
Advice
35
30
25
20
Private Generation 2
Percentage
15
10
5
Private Generation 1
0
0
5
5.5
6
6.5
Advice Left
7
7.5
8
8.5
9
10
47
Histogram of Advice Left – Private
Advice
35
30
Private Generation 3
25
20
Percentage
Private Generation 2
15
10
5
Private Generation 1
0
0
5
5.5
6
6.5
Advice Left
7
7.5
8
8.5
9
10
48
Histogram of Advice Left – Almost
Common Knowledge
Almost Common Generation 1
50
45
40
35
30
Percentage 25
20
15
10
5
Almost Common Generation 1
0
0
3
5
Advice Left
7
8
10
49
Histogram of Advice Left – Almost
Common Knowledge
50
45
40
Almost Common Generation 2
35
30
Percentage 25
20
15
10
5
0
Almost Common Generation 1
0
3
5
Advice Left
7
8
10
50
Histogram of Advice Left – Almost
Common Knowledge
Almost Common Generation 3
50
Almost Common Generation 2
40
30
Percentage
20
Almost Common Generation 1
10
0
0
3
5
Advice Left
7
8
10
51
Histogram of Advice
Common Knowledge
Common Generation 1
35
30
25
20
Percentage
15
10
5
Common Generation 1
0
0
5
6
7
7.5
Advice Left
8
8.5
9
9.5
10
52
Histogram of Advice
Common Knowledge
50
45
40
35
30
Common Generation 2
Percentage 25
20
15
10
5
Common Generation 1
0
0
5
6
7
7.5
Advice Left
8
8.5
9
9.5
10
53
Histogram of Advice
Common Knowledge
60
Common Generation 3
50
40
Common Generation 2
Percentage 30
20
10
Common Generation 1
0
0
5
6
7
7.5
Advice Left
8
8.5
9
9.5
10
54
Beliefs
• We elicit subjects’ beliefs about
round 1 contributions made by each
member of the group
• Common knowledge generates much
more exhortative advice
• This in turn creates more optimistic
beliefs
55
Implication for the
punishments literature
• In the presence of conditional
cooperators, communities may be
able to create social norms that lead
to high contribution to the public
good.
• Subjects with optimistic beliefs
about one another may be able to
sustain cooperation even without the
explicit threat of punishments.
56
Questions?
57