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Incentives and Reputation. Darwin on reputation. Man ‘ s] motive to give aid […] no longer consists of a blind instinctive impulse, but is largely influenced by the praise and blame of his fellow men. Indirect Reciprocity. Direct vs indirect reciprocity. - PowerPoint PPT Presentation
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Incentives and Reputation
Darwin on reputation
Man‘s] motive to give aid […] no longer consists of a blind instinctive impulse, but is largely influenced by the praise and blame of his fellow men.
Indirect Reciprocity
Direct vs indirect reciprocity
‚to help‘ means: confer benefit b at own cost c
Binary model
• Each player has a binary reputation G good or B bad• Individuals meet randomly, as Donor and Recipient Donor can give benefit b to Recipient at cost c• If Donor gives, Donor´s reputation G if not, Donor‘s reputation B• Discrimination: give only to G-player (SCORING) Undiscriminate stategies AllC and AllD
SCORING vs. AllC and AllD
help) intended
ngimplementinot of
ty (probabili
The paradox of SCORING
Why should one discriminate? (it reduces chances of being helped later)
Discrimination is costlyAllC can invade
Assessment
What is ‚bad‘? (rudimentary moral systems)
• SCORING: bad is to refuse help
• SUGDEN: bad is to refuse help to good player
• KANDORI: bad is (in addition) to help bad player
Assessment rules
• First order: is help given or not?• Second order: is recipient good or bad?• Third order: is donor good or bad?
• 256 assessment rules (value systems) (Ohtsuki, Iwasa; Brandt et al;2004)
Assessment rules
• First order: is help given or not?• Second order: is recipient good or bad?• Third order: is donor good or bad?
Only eight strategies lead to cooperation and cannot be invaded by other action rules, e.g. by AllC or AllD (Ohtsuki, Iwasa 2004)
Assessment
What is ‚bad‘? (rudimentary moral systems)
• SCORING: bad is to refuse help
• SUGDEN: bad is to refuse help to good player
• KANDORI: bad is (in addition) to help bad player
The leading eight
L3 (SUGDEN) and L6 (KANDORI) are second order assessment rules, the others third order
(L1 considered in Panchanathan-Boyd and Leimar-Hammerstein)
SUGDEN (or KANDORI) vs. AllC and AllD
The competition of SUGDEN and KANDORI
Must assume private image (Brandt and Sigmund, Pacheco et al)
rather than public image (Ohtsuki and Iwasa, Panchanathan and Boyd)
AllC
Kandori
Sugden
Stable fixed points(Mixture of K and S)
AllD
Incentives
Ultimatum game
Two players can share 10 euros Toss of coin decides who is proposer,
who is responderProposer offers share to ResponderResponder accepts, or declines.
What does homo oeconomicus?
If each player maximises payoff:Proposer offers minimal share,Responder accepts
What do we do?
In real life:• 60 to 80 percent of all offers between 40 et 50
percent• Less than 5 percent of all offers below 20
percent
Economic anthropology
• Henrich et al, Amer. Econ. Review 2001
Mean OfferMachiguenga 26Hazda 27Tsimamé 37Quichua 27Torguud 35Khazax 36Mapuche 34Au 43Gnau 38Sangu (Farmers) 41Achuar 42Sangu (Herders) 42Orma 44Pittsburgh 45Los Angeles 48Ache 51Lamelara 58
Variants of Ultimatum
• Against computer• Against five responders• Against five proposers
Ultimatum for mathematicians
• strategy (p,q) p size of offer, if Proposer
q aspiration level, if Responder
(percentage of total)
Mini-Ultimatum
• Only two possible offers• High offer H (40 %)• Low offer L (20 %)
Mini-Ultimatum
LL
HHHH
,10,0LProposer
,1,1HProposer
LResponder HResponder
matrix Payoff
Asymmetric Games
•
),(),(
),(),(
, strategies II,player
, strategies I,player
2
1
21
21
21
dDcCe
bBaAe
ff
ff
ee
Conditional Strategies
•
214223122111
21
21
,,,
strategies lconditiona
, strategies II, rolein
, strategies I, rolein
feGfeGfeGfeG
ff
ee
Conditional Strategies
•
M
bBdBdAbA
bDdDdCbC
aDcDcCaC
aBcBcAaA
feGfeGfeGfeG
ff
ee
2
1
,,,
strategies lconditiona
, strategies II, rolein
, strategies I, rolein
214223122111
21
21
Conditional Strategies
cdsBDSabrACR
rssr
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SSRRM
, , ,with
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columns toconstants Adding
Conditional Strategies
•
manifolds invariant
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4231
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constxx
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MxMxMxMx
Conditional Strategies
etc ),G edge(for
), edge(for ofsign on dependsn Orientatio
32
21
Gs
GGR
Mini-Ultimatum
Population of playersTypes (H,H) (social) (L,L) (asocial) (H,L) (mild) (L,H) (paradoxical)
Players copy whoever is successful
Mini-Ultimatum
),(),(),(),(
by spanned surfaces saddle
1
14321
4321
4231
HLLLLHHH
GGGGG
xxxx
xKxxx
Mini-Ultimatum
LL HL
HHLH
winner timelong ),(
),(
asocial ),(
),(
social ),(
LL
HL
LL
LH
HH
Reputation and temptation
Suppose that with a small probability
Players have information about type of co-player (reputation) and makes reduced offer L if co-player has low
aspiration level (temptation)
Mini-Ultimatum with reputation and temptation
LL
LHHLHHHH
,10,0LProposer
)(),(1,1HProposer
LResponder HResponder
Mini-Ultimatum with reputation-temptation
• Bistability
• Attractors HH (social) and LL (asocial)
LL HL
HHLH
Mini-Ultimatum with reputation-temptation
• Bistability
• Attractors HH (social) and LL (asocial)
• Social stronger if H<1/2
LL HL
HHLH
Bifurcation
LL HL
HHLH
LL HL
HHLH
Back to full ultimatum
• Evolution leads to minimal offers
(as with rational players)
With reputation-temptation to values between 40 and 50 percent
Individual-based simulations
Individual-based simulations
An economic experiment
• Ultimatum with or without reputation
• (Fehr and Fischbacher, Nature 2004)
What if someone is watching?
• Experiments by Haley, Fessler
• By Bateson et al (honesty box)
Trust Game
Investor can send amount c to Trustee, knowing it will be multiplied by factor r>1 on arrival
Trustee, on receiving b=rc, can send part of it back to Investor
Mini-Trust
)0,0()0,0(
),(),(
Payoff
c and
nothing)(return or )(return :Trustee
nothing) (give or ) (give :Investor
2
1
21
21
21
e
bcbce
ff
bcrcb
ff
ece
Mini-Trust
investment no
0
0
0
0
s
cS
r
cR
Mini-Trust with Reputation
Incentives for cooperation
First, play a donation game (or a more complex game, involving cooperation), then punish the defector or reward the cooperator
(same structure as ultimatum or trust)
PD with Reward
PD with Reward with reputation
)0,0())(,)((
))1(),1((),(
Payoff
rewarded be they willknow they if cooperate defectors that prob
oncontributi skips and l)(ungratefu isplayer -co knows
r)(cooperatoplayer - that prob.
2
1
21
2
1
bce
bcbce
ff
f
e
PD with Reward with reputation
defects) O doubt; of casein cooperates O(
O and O types two:players ticOpportunis
AllD and AllC players nalUnconditio
:stagefirst in types4
N :neither do I,both do P,Punish R, Reward
:stage secondin moves 4
:Extension
DC
DC
Payoff
Results:
],[],[],[ON][AllD,
:smaller for
],[],[],[ON][AllD,
:larger for pathway
if catalyses ],[
wins],[
D
D
POROR
POPON
bRO
PO
CC
CD
D
C
• low information
• high information