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

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Mini-Ultimatum

Population of playersTypes (H,H) (social) (L,L) (asocial) (H,L) (mild) (L,H) (paradoxical)

Players copy whoever is successful

Mini-Ultimatum

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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

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Payoff

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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

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Results:

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• high information