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A Survey of Indirect Reciprocity

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Mathematics for Ecology and Environmental Sciences

Part of the book series: Biological and Medical Physics, Biomedical Engineering ((BIOMEDICAL))

Summary

This survey deals with indirect reciprocity, i. e. with the possibility that altruistic acts are returned, not by the recipient, but by a third party. After briefly sketching how this question is dealt with in classical game theory, we turn to models from evolutionary game theory. We describe recent work on the assessment of interactions, and the evolutionary stability of strategies for indirect reciprocation. All stable strategies (the ‘leading eight’) distinguish between justified and non-justified defections, and therefore are based on non-costly punishment. Next we consider the replicator dynamics of populations consisting of defectors, discriminators and undiscriminating altruists. We stress that errors can destabilise cooperation for strategies not distinguishing justified from unjustified defections, but that a fixed number of rounds, or the assumption of an individual’s social network growing with age, can lead to cooperation based on a stable mixture of undiscriminating altruists and of discriminators who do not distinguish between justified and unjustified defection. We describe previous work using agent-based simulations for ‘binary score’ and ‘full score’ models. Finally, we survey the recent results on experiments with the indirect reciprocation game.

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References

  1. Alexander, R.D. (1987), The Biology of Moral Systems, New York: Aldine de Gruyter

    Google Scholar 

  2. Axelrod, R and Hamilton, W D (1981), The evolution of cooperation, Science 211: 1390–1396

    Article  MathSciNet  Google Scholar 

  3. Berg, J. Dickhaut, J. and McCabe, K. (1995), Trust, Recipocity and Social History, Games and Economic Behavior 10, 122–142

    Article  MATH  Google Scholar 

  4. Binmore, K G (1992), Fun and Games: a text on game theory, Health and Co, Lexington, Mass

    MATH  Google Scholar 

  5. Boerlijst, M C, Nowak, M A and K. Sigmund (1997), The logic of contrition, JTB 185: 281–294

    Article  Google Scholar 

  6. Bolton, G., Katok, K. and Ockenfels, A., (2004), Cooperation among strangers with limited information about reputation, Journal of Public Economics, in press

    Google Scholar 

  7. Bolton, G., Katok, E. and Ockenfels, A (2004), How effective are online reputation mechanisms? An experimental investigation, Management Science, in press

    Google Scholar 

  8. Bolton, G.E. and Ockenfels, A. (2000), ERC: a theory of equity, reciprocity and competition, American Economic Review 90: 166–193

    Article  Google Scholar 

  9. Boyd, R and Richerson, P J (1989), The evolution of indirect reciprocity, Social Networks 11: 213–236

    Article  MathSciNet  Google Scholar 

  10. Boyd, R and Richerson, P J (1992), Punishment allows the evolution of cooperation (or anything else) in sizeable groups, Ethology and Sociobiology 113: 171–195

    Article  Google Scholar 

  11. Brandt, H. (2004), URL: http://homepage.univie.ac.at/hannelore.brandt/ simulations Interactive java applets for online experimentation on presented simulations

    Google Scholar 

  12. Brandt, H. and Sigmund, K (2004), The logic of reprobation: assessment and action rules for indirect reciprocity, JTB, 231: 475–486

    Article  MathSciNet  Google Scholar 

  13. Brandt, H. and Sigmund, K. (2005), Indirect reciprocity, image scoring, and moral hazard, Proc. Natl. Acad. Sci. USA 102: 2666–2670

    Article  Google Scholar 

  14. Camerer, C E (2003) Behavioral Game Theory, Princeton UP

    Google Scholar 

  15. Colman, A. M. (1995) Game Theory and its Applications in the Social and Biological Sciences, Oxford: Butterworth-Heinemann.

    Google Scholar 

  16. Dawes, R. M. (1980), Social Dilemmas. Ann. Rev. Psychol. 31: 169.

    Article  Google Scholar 

  17. Dellarocas, C (2003), Efficiency and Robustness of binary feedback mechanisms in trading environments with moral hazard (working paper, MIT Sloan School of Management)

    Google Scholar 

  18. Ellison, G. (1994), Cooperation in the Prisoner’s Dilemma with anonymous random matching, Review of Economic Studies, 61: 567–588

    Article  MathSciNet  MATH  Google Scholar 

  19. Engelmann, D. and U. Fischbacher (2002), Indirect reciprocity and strategic reputation-building in an experimental helping game, working paper, Univ of Zürich

    Google Scholar 

  20. Fehr, E. and Gächter, S. (2000), Cooperation and punishment in public goods experiments. Am. Econ. Rev. 90: 980

    Article  Google Scholar 

  21. Fehr, E. and Gächter, S. (2002), Altruistic punishment in humans. Nature 415: 137

    Article  Google Scholar 

  22. Fehr, E. and Fischbacher, U. (2003), The nature of human altruism, Nature 425: 785–791

    Article  Google Scholar 

  23. Ferrière, R. (1998), Help and you shall be helped, Nature 393: 517–519

    Article  Google Scholar 

  24. Fishman, M.A. (2003), Indirect reciprocity among imperfect individuals, JTB 225: 285–292

    Article  Google Scholar 

  25. Fishman, M.A., Lotem, A. and Stone. L. (2001), Heterogeneity stabilises reciprocal altruism interaction, JTB 209: 87–95

    Article  Google Scholar 

  26. Fudenberg D and Maskin, E (1986), The folk theorem in repeated games with discounting or with incomplete information, Econometrica 50: 533–554

    Article  MathSciNet  Google Scholar 

  27. Gintis, H (2000), Game Theory Evolving, Princeton UP

    Google Scholar 

  28. Harbaugh, W T (1998), The prestige motive for making charitable transfers, American Economic Review 88: 277–282

    Google Scholar 

  29. Hofbauer, J. and Sigmund, K (1998), Evolutionary Games and Population Dynamics, Cambridge UP

    Google Scholar 

  30. Kandori, M (1992), Social norms and community enforcement, The Review of Economic Studies 59: 63–80

    Article  MATH  Google Scholar 

  31. Keser, Claudia (2002), Trust and Reputation Building in e-Commerce, Working paper, IBM Watson Research Center

    Google Scholar 

  32. Leimar, O. and Hammerstein, P. (2001), Evolution of cooperation through indirect reciprocation, Proc R Soc Lond B, 268: 745–753

    Article  Google Scholar 

  33. Lotem, A., Fishman, M A and Stone, L (1999), Evolution of cooperation between individuals, Nature 400: 226–227

    Article  Google Scholar 

  34. Lotem, A., Fishman, M A and Stone L (2002), Evolution of unconditional altruism through signalling benefits, Proc R. Soc London B, 270: 199–205

    Article  Google Scholar 

  35. Milinski, M., Semmann, D., Bakker, T.C.M. and Krambeck, H. J. (2001), Cooperation through indirect reciprocity: image scoring or standing strategy? Proc Roy Soc Lond B 268: 2495–2501

    Article  Google Scholar 

  36. Milinski, M., Semmann, D. and Krambeck, H.J. (2002a), Donors in charity gain in both indirect reciprocity and political reputation, Proc Lond Soc B 269: 881–883

    Article  Google Scholar 

  37. Milinski, M., Semmann, D. and Krambeck, H.J. (2002b), Reputation helps solve the ‘Tragedy of the Commons’, Nature 415: 424–426

    Article  Google Scholar 

  38. Mohtashemi, M. and L. Mui (2003), Evolution of indirect reciprocity by social information: the role of trust and reputation in evolution of altruism, JTB 223: 523–531

    Article  MathSciNet  Google Scholar 

  39. Nowak, M.A. and Sigmund, K (1990), The evolution of stochastic strategies in the prisoner’s dilemma, Acta Appl. Math. 20: 247–265.

    Article  MathSciNet  MATH  Google Scholar 

  40. Nowak, M.A. and Sigmund, K. (1998a), Evolution of indirect reciprocity by image scoring, Nature 282: 462–466

    Google Scholar 

  41. Nowak, M.A. and Sigmund, K. (1998b), The dynamics of indirect reciprocity, JTB 194: 561–574

    Article  Google Scholar 

  42. Ohtsuki, H (2004), Reactive strategies in indirect reciprocity, JTB 227: 299–314

    Article  MathSciNet  Google Scholar 

  43. Ohtsuki H, and Iwasa, Y (2004), How should we define goodness? — Reputation dynamics in indirect reciprocity, JTB 231: 107–120

    Article  MathSciNet  Google Scholar 

  44. Okuno-Fujiwara, M and Postlewaite, A (1995), Social Norms in Matching Games, Games and Economic Behaviour, 9: 79–109

    Article  MathSciNet  MATH  Google Scholar 

  45. Panchanathan, K. and R. Boyd (2003), A tale of two defectors: the importance of standing for evolution of indirect reciprocity, JTB 224: 115–126

    Article  MathSciNet  Google Scholar 

  46. Pollock, G B and L A Dugatkin (1992), Reciprocity and the evolution of reputation, JTB 159: 25–37

    Article  Google Scholar 

  47. Rosenthal, R W (1979), Sequences of games with varying opponents, Econometrica 47: 1353–1366

    Article  MathSciNet  MATH  Google Scholar 

  48. Seinen, I. and Schram, A. (2001), Social status and group norms: indirect reciprocity in a helping experiment, working paper, CREED, Univ. of Amsterdam

    Google Scholar 

  49. Semmann D, Krambeck, H J and Milinski, M (2004), Strategic investment in reputation, J Behav. Ecol. Sociobiol. 56: 248–252

    Google Scholar 

  50. Sheratt, T N and Roberts, G (2001), The importance of phenotypic defectors in stabilising reciprocal altruism, Behav. Ecol. 12: 313–317

    Article  Google Scholar 

  51. Sigmund, K., Hauert, C., and Nowak, M. A. (2001), Reward and punishment. Proc. Natl. Acad. Sci. 98: 10757–10763

    Article  Google Scholar 

  52. Sugden, R. (1986), The Economics of Rights, Cooperation and Welfare, Basil Blackwell, Oxford

    Google Scholar 

  53. Takahashi, N. and R. Mashima (2004), The importance of indirect reciprocity: is the standing strategy the answer? Working Paper Hokkaido Univ

    Google Scholar 

  54. Trivers, R (1971), The evolution of reciprocal altruism, Quart Rev Biol 46, 35–57

    Article  Google Scholar 

  55. Wedekind, C and Milinski, M (2000), Cooperation through image scoring in humans, Science 288, 850–852

    Article  Google Scholar 

  56. Wedekind, C (1998), Give and ye shall be recognised, Science 280: 2070–2071

    Article  Google Scholar 

  57. Wedekind, C. and Braithwaite, V.A. (2002), The long-term benefits of human generosity in indirect reciprocity, Curr Biol. 12: 1012–1015

    Article  Google Scholar 

  58. van der Heijden, E C M (1996), Altruism, Fairness and Public Pensions, PhD thesis Amsterdam

    Google Scholar 

  59. Zahavi, A (1995), Altruism as a handicap — the limitations of kin selection and reciprocity, J Avian Biol 26: 1–3

    Google Scholar 

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Nordbergstrasse 15, 1090, Wien, Austria

    Hannelore Brandt & Karl Sigmund

  2. Department of Biology, Faculty of Sciences, Kyushu University, Japan

    Hisashi Ohtsuki & Yoh Iwasa

Authors
  1. Hannelore Brandt
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  2. Hisashi Ohtsuki
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  3. Yoh Iwasa
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  4. Karl Sigmund
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Editor information

Editors and Affiliations

  1. Faculty of Engineering Department of Systems Engineering, Shizuoka University, Hamamatsu 3-5-1, 432-8561, Shizuoka, Japan

    Yasuhiro Takeuchi  & Kazunori Sato  & 

  2. Department of Biology, Kyushu University, 812-8581, Fukuoka, Japan

    Yoh Iwasa

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Brandt, H., Ohtsuki, H., Iwasa, Y., Sigmund, K. (2007). A Survey of Indirect Reciprocity. In: Takeuchi, Y., Iwasa, Y., Sato, K. (eds) Mathematics for Ecology and Environmental Sciences. Biological and Medical Physics, Biomedical Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-34428-5_3

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