Experiment
Jakub Caisl
Outline
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Introduction
Related literature
Motivation
Experimental design
Hypothesis, outcomes
Possible extensions
Resources
Introduction
• Public goods dilemma – cooperation more
profitable for the whole group but individually
it pays to free-ride on effort of others
• Studied widely in experimental literature,
Public goods game
• Evidence that cooperation falls over time to
very low levels (Ledyard, 1994; Zellner, 2003)
Introduction 2
• Trend reversed when punishment introduced
(Gächter & Fehr, 2000), cooperation doesn´t
fall over time
• Punishment not only motivated strategically,
also concerns for fairness, anger,… (Fehr &
Fischbacher,2003; Falk et al., 2005)
• The punishment effect on cooperation very
sensitive to information about behaviours of
others and on punishment possibilities
Related literature – Imperfect
monitoring
• Results of punishment sensitive to noise in
information (Grechenig et al, 2010; Ambrus &
Greiner, 2011)
• Concept of free-rider anonymity (Patel et al.,
2010)
• Collective punishment by external authority that
only observes group results (Dickinson,
forthcoming)
• Visibility of endowments (Bornstein & Wiesel,
2010)
Related literature – Punishment
possibilities
• Efficiency of punishment conditional on how
large a fraction of subjects can be punished
(Carpenter, 2004)
• Also dependedent on the structure of
punishment and monitoring possibilities
(Carpenter, 2010)
Differences with related literature
• No noise, no free-rider anonymity, no
asymmetric endowments
• Related most closely to network literature –
but we limit only monitoring options, not
punishment options
Explanation of basic terms
• Network – a structure of monitoring of
individuals in the group – often expresses very
limited possibilities of monitoring
• Examples from Schotter:
Explanation of basic terms 2
• Network can be:
– Complete: each pair of nodes conneceted by an
edge
– Connected: if each pair of players linked by a path
– Directed: if at least one pair of players is not
connected symetrically
– Degree of a node: number of edges that stem
from the node (out-degree) and are pointed at the
node (in-degree)
Motivation
• Monitoring behaviour often limited to people
the observer meets often
• Punishment often restricted by external
authorities (legal system)
• Related to:
– Monitoring strategies in work-teams
– Social settings – everyone observed, disconnected
minority, hierarchical structure
Motivation
• Necessary in such context to limit punishment
behaviour to the people one observes?
• Costs of enforcing restrictions on punishment
behaviour (legal systems)
• Do people punish without observing?
• Is it damaging or can it at times be helpful?
Experimental design
• Public goods game with punishment
• 4 Players (Type A, B, C, D, constant through
game)
• MPCR = 0.4
• Cost of punishment (reduction by 1 token) c =
0.5
• 15 periods (10?)
• Strangers
Experimental design 2
• Two stages
– 1st stage:
• contributions to public accounts
• contributions of those connected to in network
observed
• total group contributions observed
• elicitation of beliefs about others contributions before
second stage begins.
– 2nd stage: punishment based on information from
previous stage, at the end own payoff observed
Explanation of basic terms
• Types of players involved
– Free rider – purely selfish, 0 contributions more than
half of the time, 0 punishment, little sensitivity to
punishment
– Conditional cooperator – contributions linked to
group average (Gächter, 2006), 0 punishment,
sensitive to punishment
– Strong reciprocator (Fehr & Gintis, 2007) contributions linked to group average, willing to
punish defectors at net cost to himself, sensitive to
punishment
Explanation of basic terms
• Unsure punishment
– Punishing people one doesn´t directly observe
– Simple to create expectations about contributions of
others (testable on elicited beliefs)
j
E (Ci ) =
–
–
–
–
CT − ∑ C j
1
4− j
CT : Total group contributions in current round
Cj : Contribution of observed individual j
E(Cj) : Expected contribution of unobserved individual i
j : Number of observed individuals
Explanation of basic terms
• Unsure punishment
– Not as desirable as sure punishment, punishment towards
defectors (social) be misdirected to contributors
(antisocial)
U i = π i + p ( δ i ) + (1 − p )( − δ i )
– Antisocial punishment lowers contributions of those
afflicted
– In particular if C − ∑C :
j
T
1.
2.
3.
j
1
lower than group average contribution – more social punishment
lower than twice the group average contribution – more social
and antisocial punishment
higher than twice the group average contribution – antisocial
punishment
Explanation of basic terms
• Unsure punishment – motivation
– Negative reciprocity (Falk & Fischbacher, 2006) often
emotionaly driven (Fehr & Fischbacher, 2003; Falk,
Fehr & Fischbacher, 2005; Fehr & Gächter, 2000)
– If not enough opportunities for sure punsihment, one
might resort to unsure punishment
– Individual has to satisfy:
• Proportionality of the punishment (Fehr & Gächter, 2000)
• Strong reciprocal motivation
Treatments
• Treatments vary in networks used, with
respect to connectedness – minimal possible
variations
• In total three treatments (possible extensions)
• Treatment (only information restricted) vs.
Control (both information and punishment
restricted in the same way)
Treatment 1 – Directed circle
• Directed, fully connected network
• Everyone faces the same conditions
• Control: Connectedness + directedness = most
punishment, contributions and efficiency
Treatment 1 – Punishment
(Strong reciprocators)
1. Type 1 unsure punishment – more social punishment
2. Type 2 unsure punishment – both more social and
antisocial punishment
3. Breaking the directedness of network – coordination
problem, responsibility – less social punishment
(Carpenter, 2010; measure strenght of sure
punishment conditional on punishing)
• Everyone one in-degree and out-degree, symmetric
• Directedness has very strong effect on punishment
(Carpenter, 2010), unsure punishment less efficient
than sure punishment – 3. overrides 1., 2.
Outcome 1 - Punishment
• Outcome 1: „With unrestircted punishment
there will be in general less punishment in
treatment 1 when compared to control, in
particular more antisocial and less social
punishment.“
Treatment 1 - Contributions
• Less social punishment – less contributions
• Less reaction to social punishment – less
contributions
• More antisocial punishment – less
contributions
Outcome 2
• Outcome 2: „In treatment one there will be
less contributions than in control.“
• But less sensitivity to social punishment,
antisocial punishment
• Measure: Total amount of contributions,
sensitivity to punishment, effect of antisocial
punishment, relation to total amount of social
punishment (the same for other treatments)
Summary Table
Type of player
Free rider
Conditional
cooperator
Strong
reciprocator
Total effect of
given
influence
Total effect on
punishment,
contributions
Comparison of treatment 1 with control 1 in terms of received punishment and contributions
Received punishment
Effect on contributions
Type 2
Type 1
Breaking
Type 1 unsure
Type 2 unsure
Breaking
unsure
unsure
directedness
directedness
punishment
punishment
punishment
punishment
No reaction to
No reaction to
No reaction to
received punishment,
received
received
can become a
More social
punishment
punishment
conditional cooperator
punishment
!Less social
More social
More contributions
More
punishment! punihsment
!Less
due to social
antisocial
contributions,
punishment
punishment
More contributions
can become a
Less contributiopns
free rider!
due to antisocial
punishment
!Less social
More social
More social
!Less
More contributions,
Ambiguous
punishment! punishment
punishmet
contributions, less free riders
More
more free
antisocial
riders!
punihsment
•
Less punishment
•
Less social punishment
•
Less contributions
•
More antisocial punishment
Treatment 1 - Efficiency
• Less punishment – more efficiency
• Less contributions – less efficiency
• Antisocial punishment – less efficiency
Outcome 3
• Outcome 3: „In tretament 1 there will be less
efficiency than in control.“
• But efficiency improved with less punishment
Treatment 2 – Disconnected directed
circle
• Directed, disconnected network
• Hierarchical strucuture
• Control 2: Disconneted + directed = lowest
punishment, contributions and efficiency
Treatment 2 – Punishment (strong
reciprocators)
• Players B, C – one in-degree, on out-degree
• Player A – one out-degree
• Player D – one in degree
Unsure punishment
– Expectations no longer just
C − ∑C
j
E (Ci ) =
T
j
1
4− j
– Expectations of low contributions skewed towards
player A – unobserved (testable on elicited beliefs)
Treatment 2 - Punishment (Strong
reciprocators)
1. Type 1 punishment, Type 2 punishment – more
often than treatment 1 because:
–
–
–
player A unobserved and responsible(players B,C,D)!
no sure punishment (player D),
mitigated by no responsibility for punishment of
player D (players A,B)
2. Break directedness – no significant effect since
network not connected (measure strenght of
punishment)
• 1. Restores connectedness – possible indirect
increase of sure punishment in A,B,C
Outcome 4
• Outcome 4: „There will be more punishment in
treatment 2 than in control 2, both in terms of
social and antisocial punishment.“
Treatment 2 - Contributions
1. Connectedness – more contributions
– more social punishment (Type1, Type2),
– improved conditional cooperation
2. Less sensitivity to punishment – less
contributions
3. More antisocial punishment – less contributions
• Connectedness very important in networks – 1.
dominates but 3. can also be quite important
Outcome 5
• Outcome 5: „The contributions in treatment 2
are higher than in control 2.“
• But antisocial punishment, less sensitivity to
social punihsment
Summary table
Type of player
Free rider A,
Conditional
cooperator A
Comparison of treatment 2 with control 2 in terms of received punishment and contributions
Received punishment
Effect on contributions
Breaking Type 1
Type 2
Breaking
Type 1 unsure
Type 2 unsure
directedn unsure
unsure
directedness punishment
punishment
ess
punishment punishment
No reaction to received
No reaction to received
!More social
punishment, !can
No
punishment!
punishment, can become
become a conditional
!More social
significan
More
a conditional cooperator
cooperator!
punishment!
t effect
antisocial
punishment
!More contributions!
More contributions
Free rider B,C,D
Strong
reciprocator A
Conditional
cooperator B,C,D
Strong
reciprocator B, C,
D
No
significan
t effect
No effect
Total effect of
given influence
Total effect on
punishment,
contributions
•
•
•
More social
punishment
More social
punishment
More
antisocial
punishment
!More social !More social
punishment! punishmet!
More
antisocial
punihsment
More punishment
More antisocial punishment
Irestored connectednesssincrease of social punihsment
No
signifficant
effect
No effect
•
No reaction to received
punishment, can
become a conditional
cooperator
No reaction to received
punishment
More contributions
More contributions due to
social punishment
Less contributiopns due to
antisocial punishment
!More contributions,
less free riders!
More contributions
•
More contributions
Restored connectedness - increased conditional cooperation,
more contributions
Treatment 2 Efficiency
• More punishment – less efficiency
• More contributions – more efficiecy
• Antisocial punishment – less efficiency
Outcome 6
• Outcome 6: „Tretament 2 will be more
efficient than control 2, since connectedness of
the network will be restored“.
• But antisocial punishment
Treatment 3 – Partially connected
directed circle
• Directed, subgroup connected network
• Everyone faces the same conditions, but there
is a disconnected minority
• Control 3: Partial connectedness +
directedness = lower punishment,
contributions, efficiency than treatment 1
Treatment 3 Punishment (Strong
reciprocators)
• Players A, B, C – one in-degree, on out-degree
• Player D – no degree, key difference to tratment
2, no responisbility in network
Unsure punishment
– Expectations player D:
j
E (Ci ) =
CT − ∑ C j
1
4− j
– But expectations of players A,B,C of low contributions
skewed towards player D – unobserved (testable on
elicited beliefs)
Treatment 3 – Punishment (Strong
reciprocators)
1. Type 1 punishment, Type 2 punishment – more
than treatment 1, less than treatment 2:
1. player A unobserved but no responsibility(players
A,B,C)!
2. no sure punishment (player D)
2. Break directedness in subgroup – lower amount
of social punishment (players A,B,C – measure
strenght of p.)
3. Group affiliation – possible further extension
• 1. can restore connectedness- Clash between 1.
and 2., we assume that 1. is stronger
Outcome 7
• Hypothesis 3: „There will be more punishment
in treatment 3 than in control 3, in particular
there will be at least as much social
punishment and more antisocial punishment.“
• But breaking directedness can dominate
reaching connectedness, in such case less
punishment
Treatment 3 - Contributions
1. Reaching connectedness – more contributions
– more social punishment
– possibly improved conditional cooperation
2. Breaking directedness – less social punishment less contributions
3. Less sensitivity to punishment – less
contributions
4. More antisocial punishment – less contributions
• 1. clashes with 2. , 4. possibly quite important –
the same or less contributions than control 3
Outcome 8
• Outcome 5: „The contributions in treatment 2
are the same or lower than in control 2.“
• But reaching connectedness can have more
positive effects
Summary table
Type of player
Free rider D,
Conditional
cooperator D
Comparison of treatment 3 with control 3 in terms of received punishment and contributions
Received punishment
Effect on contributions
Type 1
Type 2
Breaking
Breaking
Type 1 unsure
unsure
unsure
Type 2 unsure punishment
directedness
directedness
punishment
punishment
punishment
No reaction to received
More social
No reaction to received
punishment, !can
No
punishment
punishment, can become
!More social
No significant
become a conditional
significant
More
conditional cooperator
punishment!
effect
cooperator!
effect
antisocial
punishment
!More contributions!
More contributions
Free rider
A,B,C
Strong
reciprocator A
Conditional
cooperator
A,B,C
Strong
reciprocator
A,B, C
Total effect
of given
influence
Total effect
on
punishment,
contributions
!Less social
punishment!
!Less social
punishment!
•
•
More social
punishment
!More social
punishment!
More social
punishment
More
antisocial
punishment
More social
punishmet
More
antisocial
punihsment
More/same social punishment
More antisocial punishment
!Less
contributions,
can become a
free rider!
!Less
contributions,
more free
riders!
•
No reaction to received
punishment, can become
a conditional cooperator
No reaction to received
punishment
More contributions
More contributions due to
social punishment
Less contributiopns due to
antisocial punishment
!More contributions,
less free riders!
Ambiguous
•
Same or less contributions
Restored connectedness - increased conditional cooperation,
more contributions
Treatment 3 Efficiency
• More punishment – less efficiency
• Same or less contributions – less efficiency
• Antisocial punishment – less efficiency
Outcome 9
• Outcome 9: „Treatment 3 will be less efficient
than Control 3“
• But reaching connectedness can bring more
gains
Hypothesis 1
• Hypothesis 1: „The change of punishment in
treatment versus control depends on the
connectedness of the network. The less
connected the network is , the more (less) the
punishment will increase (decrease).“
• But reaching connectedness irrelevant when
very little information
• Measure: Compare the change of punishment
with respect to control among all treatments.
Hypothesis 2
• Hypothesis 2: „The change of contributions in
treatment versus control depends on the
connectedness of the network. The less
connected the network is , the more (less) the
contributions will increase (decrease).“
• Measure: Compare the change of
contributions with respect to control among
all treatments.
Hypothesis 3
• Hypothesis 3: „The change of efficiency in
treatment versus control depends on the
connectedness of the network. The less
connected the network is , the more (less) the
efficiency will increase (decrease).“
• Measure: Compare the change of efficiency
with respect to control among all treatments.
Extensions
• Group affiliation
Player
A
Player
B
Player
C
Player
D
Extensions
• Everyone one in-degree, one out-degree
• Non-directed, non-conected but perfectly
subconnected, everyone observed
• Could very well be comparable with directed
circle
• Unsure punishment compared to directed
circle – could show group affilitation if
relevant (Tajfel)
Resources
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