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Incentives and Reputation

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.

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Incentives and Reputation

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  1. Incentives and Reputation

  2. 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.

  3. Indirect Reciprocity

  4. Direct vs indirect reciprocity ‚to help‘ means: confer benefit b at own cost c

  5. 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

  6. SCORING vs. AllC and AllD

  7. The paradox of SCORING Why should one discriminate? (it reduces chances of being helped later) Discrimination is costly AllC can invade

  8. 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

  9. 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)

  10. 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)

  11. 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

  12. 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)

  13. SUGDEN (or KANDORI) vs. AllC and AllD

  14. 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)

  15. AllC AllD Sugden Stable fixed points (Mixture of K and S) Kandori

  16. Incentives

  17. 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.

  18. What does homo oeconomicus? • If each player maximises payoff: • Proposer offers minimal share, • Responder accepts

  19. 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

  20. Economic anthropology • Henrich et al, Amer. Econ. Review 2001

  21. Variants of Ultimatum • Against computer • Against five responders • Against five proposers

  22. Ultimatum for mathematicians • strategy (p,q) p size of offer, if Proposer q aspiration level, if Responder (percentage of total)

  23. Mini-Ultimatum • Only two possible offers • High offer H (40 %) • Low offer L (20 %)

  24. Mini-Ultimatum

  25. Asymmetric Games

  26. Conditional Strategies

  27. Conditional Strategies

  28. Conditional Strategies

  29. Conditional Strategies

  30. Conditional Strategies

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

  32. Mini-Ultimatum

  33. Mini-Ultimatum

  34. 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)

  35. Mini-Ultimatum with reputation and temptation

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

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

  38. Bifurcation

  39. Back to full ultimatum • Evolution leads to minimal offers (as with rational players) With reputation-temptation to values between 40 and 50 percent

  40. Individual-based simulations

  41. Individual-based simulations

  42. An economic experiment • Ultimatum with or without reputation • (Fehr and Fischbacher, Nature 2004)

  43. What if someone is watching? • Experiments by Haley, Fessler • By Bateson et al (honesty box)

  44. 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

  45. Mini-Trust

  46. Mini-Trust

  47. Mini-Trust with Reputation

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