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

The paradox of SCORING Why should one discriminate? (it reduces chances of being helped later) Discrimination is costly AllC 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 AllD Sugden Stable fixed points (Mixture of K and S) Kandori

Incentives

Ultimatum game Two players can share 10 euros Toss of coin decides who is proposer, who is responder Proposer offers share to Responder Responder 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

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

Asymmetric Games

Conditional Strategies

Conditional Strategies

Conditional Strategies

Conditional Strategies

Conditional Strategies

Mini-Ultimatum Population of players Types (H,H) (social) (L,L) (asocial) (H,L) (mild) (L,H) (paradoxical) Players copy whoever is successful

Mini-Ultimatum

Mini-Ultimatum

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

Mini-Ultimatum with reputation-temptation Bistability Attractors HH (social) and LL (asocial)

Mini-Ultimatum with reputation-temptation Bistability Attractors HH (social) and LL (asocial) Social stronger if H<1/2

Bifurcation

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

Mini-Trust

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

PD with Reward with reputation

 

Payoff

Results:

low information high information