emergence of cooperation in group interactions: avoidance vs restriction
TRANSCRIPT
Introduction Restriction vs Avoidance Participation Conclusions
Emergence of Cooperation in Group Interactions:Avoidance vs Restriction
The Anh Han1 Luıs Moniz Pereira2 Tom Lenaerts 3,4
1Teesside University, 2Universidade Nova de Lisboa3Universite Libre de Bruxelles & 4Vrije Universiteit Brussel,
ECMAI, Stanford University21-23 March, 2016
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Introduction Restriction vs Avoidance Participation Conclusions
Outline
1. Introduction• The problem of the evolution of cooperation• Cooperation in Public Goods Game
2. Two models of commitment in Public Goods Game• Restriction and avoidance• Levels of participation
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Introduction Restriction vs Avoidance Participation Conclusions
What is Cooperation?
• pay a cost for someone else to receive a benefit.
• Cooperation is widespread: insects, hunter-gatherer societies,team work, international relationships, etc.
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Introduction Restriction vs Avoidance Participation Conclusions
Paradox of cooperation
If natural selection is based on competition, how can it lead to cooperation?
• Natural selection: only the fittestsurvive
• Everyone wants to increase theirfitness.
• No one wants to pay the cost,happily accepting benefits.
• Dilemma: everyone would bebetter off cooperating with eachother (benefit > cost).
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Introduction Restriction vs Avoidance Participation Conclusions
Interdisciplinary research
• Understanding the evolution of cooperation remains afundamental challenge, for scientists from fields likeevolutionary biology, physics, economics, mathematics,computer science1, etc.
• Many fields ... same math!!
• Mathematical Framework: Evolutionary Game Theory
• Metaphors: Prisoner’s dilemma, Public Goods Game,Ultimatum game, etc.
1IJCAI, AAMAS, CEC, GECCO, ALIFE, COGNITION5 / 35
Introduction Restriction vs Avoidance Participation Conclusions
Evolutionary Game Theory
payoff → fitness → social success
Natural selection leads to the destruction ofcooperation (tragedy of commons).
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Why arrange commitments?
• Sometimes difficult to predict others’ behavior orrecognize their intentions with sufficient confidence.
• Commitment proposal can help clarify intentions of others.• contracts, marriage, apartment rental, etc.
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Introduction Restriction vs Avoidance Participation Conclusions
Why arrange commitments?
• Sometimes difficult to predict others’ behavior orrecognize their intentions with sufficient confidence.
• Commitment proposal can help clarify intentions of others.• contracts, marriage, apartment rental, etc.
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Introduction Restriction vs Avoidance Participation Conclusions
From pairwise 2 3 4 to group commitment
2Han, Pereira, Santos. Emergence of commitment and cooperation. AAMAS, 2012.
3Han, Pereira, Santos, Lenaerts. Good agreements make good friends. Nature Scientific Reports, 2013.
4Han, Santos, Lenaerts, Pereira. Synergy between intention recognition and commitments in cooperation
dilemmas. Nature Scientific Reports, 2015.
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Introduction Restriction vs Avoidance Participation Conclusions
Group commitment applications
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Introduction Restriction vs Avoidance Participation Conclusions
The Public Goods Game (PGG)
• Group size N.
• Cooperator contributes c .
• Free-rider contributes nothing.
• Enhancement factor r < N.
• The common good is sharedequally among all players.
• Free-rider’s payoff: r×Nc×cN
• Cooperator’s payoff: r×Nc×cN − c
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Introduction Restriction vs Avoidance Participation Conclusions
The Public Goods Game (PGG)
• Group size N.
• Cooperator contributes c .
• Free-rider contributes nothing.
• Enhancement factor r < N.
• The common good is sharedequally among all players.
• Free-rider’s payoff: r×Nc×cN
• Cooperator’s payoff: r×Nc×cN − c
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Introduction Restriction vs Avoidance Participation Conclusions
The Public Goods Game (PGG)
• Group size N.
• Cooperator contributes c .
• Free-rider contributes nothing.
• Enhancement factor r < N.
• The common good is sharedequally among all players.
• Free-rider’s payoff: r×Nc×cN
• Cooperator’s payoff: r×Nc×cN − c
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Introduction Restriction vs Avoidance Participation Conclusions
Restriction vs Avoidance of non-committers
• What to do when other players do not commit to the groupeffort?
• Refusing to participate removes benefits from free-riders, butalso from those who are willing to join and contribute.
• Restricting access of non-committers to public goods needsextra effort.
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Introduction Restriction vs Avoidance Participation Conclusions
Commitment proposing strategies
AVOID contributes if everyone in thegroup commit, otherwise does notcontribute.
RESTRICT sets up extra measureto restrict access of non-committers tothe PGG.
• commitment proposers share aset-up cost, εP .
• compensation from dishonoredcommitters, δ.
• extra measure set-up cost, εR
• restriction for non-committers,Ψ < 1
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Introduction Restriction vs Avoidance Participation Conclusions
Commitment proposing strategies
AVOID contributes if everyone in thegroup commit, otherwise does notcontribute.
RESTRICT sets up extra measureto restrict access of non-committers tothe PGG.
• commitment proposers share aset-up cost, εP .
• compensation from dishonoredcommitters, δ.
• extra measure set-up cost, εR
• restriction for non-committers,Ψ < 1
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Introduction Restriction vs Avoidance Participation Conclusions
What are the strategies of the co-players
• Cooperator (C): always acceptscommitment.
• Defector (D): never acceptscommitment.
• Fake committer (FAKE): acceptscommitment, yet defects in game.
• Commitment free-rider (FREE): accepts commitment andcooperates, yet defects when receiving no commitmentproposal.
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Introduction Restriction vs Avoidance Participation Conclusions
AVOID non-committers promotes cooperation
AVOID64%
C10%
D19%
FAKE1%
1.9ρN
4.2ρN
4.2ρN
51.8ρN
FREE6%
4.2ρN
8.0ρN
1.4ρN
δ
εP
0.70
0.28
0.63 0.21
0.14
0.49
0.56
0.42
0.35
0.07
10
Parameters: εP=0.25; δ=2; r = 3; N = 5
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Introduction Restriction vs Avoidance Participation Conclusions
... but RESTRICT can do better
𝛹
0.24
0.14
0.43
0.62
0.570.38
0.28
0.480.19
0.33
εR
10
0.72 0.67
εR
εP
𝛹
N�1X
k=1
k(1� ) N + k(1� )
rc � FN ✏R + FN�1✏P + (N � 1)c
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Introduction Restriction vs Avoidance Participation Conclusions
εR εR
N=5 N=10
N=20 N=100
r = 6
εR εR
𝛹
𝛹
N=5 N=10
N=20 N=100
r = 3
r = 12
εR εR
N=5 N=10
N=20 N=100
r = 24
εR εR
N=5 N=10
N=20 N=100
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Introduction Restriction vs Avoidance Participation Conclusions
Remark 5.
• Both commitment strategies can promote evolution ofcooperation in PGG when the cost of arranging commitmentis justified with respect to the benefit of cooperation.
• RESTRICT is better than AVOID if non-committers can beefficiently restricted, especially for beneficial PGG.
5Han, Pereira, Lenaerts. Avoiding or restricting defectors in public goods games? Royal Soc Interface, 2015.
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Introduction Restriction vs Avoidance Participation Conclusions
Group level of participation
• How many participants need to commit to start the venture?
• Multiple intermediate degrees of group commitment arepossible.
• Minimum membership requirement is standard in internationalagreement (Montreal protocol – 11 countries 1989; KyotoProtocol – 55 parties 2005; Paris agreement: expected 85)
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Commitment strategy
COMP(F) contributes if thereare at least F players in thegroup commit, otherwise doesnot contribute.
There are as many commit-ment proposing strategies as thegroup size: 1 ≤ F ≤ N.
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Introduction Restriction vs Avoidance Participation Conclusions
What are the strategies of the co-players
• Cooperator (C): always acceptscommitment.
• Defector (D): never acceptscommitment.
• Fake committer (FAKE): acceptscommitment, yet defects in game.
• Commitment free-rider (FREE): accepts commitment andcooperates, yet defects when receiving no commitmentproposal.
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Introduction Restriction vs Avoidance Participation Conclusions
Emergence of cooperation and commitment
0.94
0.86
0.77 0.69
0.57
0.45
0.2 0.12
0.84
0.75
0.67 0.5
0.42
0.33
Cooperation frequency Commitment frequency
Arrangement cost, ε Arrangement cost, ε
mul
tiplic
atio
n fa
ctor
, r
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Introduction Restriction vs Avoidance Participation Conclusions
How many members need to commit?
F* = 2
Arrangement cost, ε
3.6
3.5
3.4
3.3
3.2
F* = 3
F* = 4
F* = 5
a b
Arrangement cost, ε
mul
tiplic
atio
n fa
ctor
, r
Average commitment level Optimal commitment strategy
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Introduction Restriction vs Avoidance Participation Conclusions
Public Goods Game Experiments with Commitments
• Prior-deposit model [Cherry and McEvoy, 2013]:• Centralized party arranging the commitment.• Commitment threshold F is decided externally.• Best to ask for full group commitment (F = N) (experiments).• Our model is modified to capture this experiment setting and
results comply with this observation.
• Forced cooperation model [Chen and Komorita, 1994]: onceagreed to cooperate, forced to cooperate.
• FAKE is equivalent to FREE.• Four strategies model: 60% cooperation, similar to data.
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Introduction Restriction vs Avoidance Participation Conclusions
Public Goods Game Experiments with Commitments
• Prior-deposit model [Cherry and McEvoy, 2013]:• Centralized party arranging the commitment.• Commitment threshold F is decided externally.• Best to ask for full group commitment (F = N) (experiments).• Our model is modified to capture this experiment setting and
results comply with this observation.
• Forced cooperation model [Chen and Komorita, 1994]: onceagreed to cooperate, forced to cooperate.
• FAKE is equivalent to FREE.• Four strategies model: 60% cooperation, similar to data.
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Introduction Restriction vs Avoidance Participation Conclusions
Remarks 6
• Conclusions for pairwise commitments can be generalized togroup commitments (regarding arrangement cost andcompensation).
• In multi-player games, an intermediate commitment isemerged.
• The more beneficial the cooperation and the lower cost ofarranging commitment, a lower degree of commitment fromother members will be required.
• Complying with behavioral experimental data.
6Han, Pereira, Lenaerts. Evolution of Commitment and Level of Participation in Public Goods Games. In
Revision for JAAMAS.
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Introduction Restriction vs Avoidance Participation Conclusions
Conclusions
• Commitment strategies can promote cooperation if itsarrangement is well facilitated.
• Restricting non-committers’ access to the public goods ismore advantageous if it is facilitated (small cost, high effect).
• Otherwise, it is important to look at the level of participationdepending on different factors.
• Implications: insights into design of self-organized anddistributed MAS where agents work in team (e.g. multi-robotsystems).
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Introduction Restriction vs Avoidance Participation Conclusions
Conclusions
• Commitment strategies can promote cooperation if itsarrangement is well facilitated.
• Restricting non-committers’ access to the public goods ismore advantageous if it is facilitated (small cost, high effect).
• Otherwise, it is important to look at the level of participationdepending on different factors.
• Implications: insights into design of self-organized anddistributed MAS where agents work in team (e.g. multi-robotsystems).
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Introduction Restriction vs Avoidance Participation Conclusions
Thank you!
QUESTIONS?
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Introduction Restriction vs Avoidance Participation Conclusions
Viability of COMP(F)
1.8ρN
16%
14%
12%6%4.3ρN
85.0ρN
D16%
F = 3
F = 5
F = 4
F = 1 F = 2
FREE0%
C16%
FAKE0%
2.6ρN
3.4ρN
5.7ρN
5.7ρN
5.7ρN
10.1ρN
46.3ρN
18%
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Introduction Restriction vs Avoidance Participation Conclusions
Optimal F for varying ε and δC
ompe
nsat
ion
cost
, δ
r = 2.5
Arrangement cost, ε
F* = 3 F* = 4
r = 4.0
F* = 4 F* = 5
Arrangement cost, ε
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Introduction Restriction vs Avoidance Participation Conclusions
Varying group sizes
Arrangement cost, ε
Com
pens
atio
n co
st, δ
N = 5 N = 7 N = 9
N = 15N = 13N = 11
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