The European Physical Journal B

, Volume 73, Issue 4, pp 625–632 | Cite as

Cooperation evolution in random multiplicative environments

Interdisciplinary Physics


Most real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of the parameters determining their dynamics. These empirical systems are in many cases subject to noise of multiplicative nature. The special properties of multiplicative noise as opposed to additive noise have been noticed for a long while. Even though apparently and formally the difference between free additive vs. multiplicative random walks consists in just a move from normal to log-normal distributions, in practice the implications are much more far reaching. While in an additive context the emergence and survival of cooperation requires special conditions (especially some level of reward, punishment, reciprocity), we find that in the multiplicative random context the emergence of cooperation is much more natural and effective. We study the various implications of this observation and its applications in various contexts.


Independent Realization Cooperation Evolution Total Wealth Multiplicative Process Sharing Individual 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. R.J. Aumann, M. Maschler, Repeated Games with Incomplete Information (MIT Press, Cambridge, MA, 1995) Google Scholar
  2. G. Hardin, Science 162, 1243 (1968) Google Scholar
  3. M.A. Nowak, Science 314, 1560 (2006) Google Scholar
  4. J. von Neumann, O. Morgenstern, Theory of Games and Economic Behavior (Princeton University Press., 1944) Google Scholar
  5. M. Allais, Econometrica 21, 503 (1953) Google Scholar
  6. D. Kahneman, A. Tversky, Econometrica 47, 313 (1979) Google Scholar
  7. R.H. Thaler, Quasi Rational Economics (Russell Sage Foundation Publications, 1994) Google Scholar
  8. G.W. Kim, H.M. Markowitz, J. Portfolio Manag. 16, 4552 (1989) Google Scholar
  9. M. Marsili, S. Maslov, Y.C. Zhang, Physica A 253, 403 (1998) Google Scholar
  10. S.N. Ethier, Journal of Applied Probability 41, 1230 (2004) Google Scholar
  11. B. Derrida, Non-self-averaging effects in sums of random variables, spin glasses, random maps and random walks (Plenum Press, New York, 1994), pp. 125–137 Google Scholar
  12. J. Kelly, Bell System Technology Journal 35, 917 (1956) Google Scholar
  13. L.M. Rotando, E.O. Thorp, The American Mathematical Monthly 99, 922 (1992) Google Scholar
  14. E.O. Thorp, Revue de l’Institut International de Statistique/Review of the International Statistical Institute 37, 273 (1969) Google Scholar
  15. R. Vince, The Mathematics of Money Management: Risk Analysis Techniques for Traders (John Wiley & Sons, Inc., New York, 1992) Google Scholar
  16. B.L. Miller, Management Science 22, 220 (1975) Google Scholar
  17. H.M. Markowitz, The Journal of Finance 31, 1273 (1976) Google Scholar
  18. S. Browne (2000), pp. 215–231 Google Scholar
  19. D.C. Aucamp, Management Science 39, 1163 (1993) Google Scholar
  20. P.H. Algoet, T.M. Cover, The Annals of Probability 16, 876 (1988) Google Scholar
  21. M. Medo, Y.M. Pis’mak, Y.C. Zhang, Physica A 387, 6151 (2008), arXiv:0803.1364v2 Google Scholar
  22. L. Lehmann, L. Keller, J. Evol. Biol. 19 (2006) Google Scholar
  23. R. Axelrod, W.D. Hamilton, Science 211, 1390 (1981) Google Scholar
  24. S. Redner, American Journal of Physics 58, 267 (1990) Google Scholar
  25. Z.F. Huang, S. Solomon, Physica A Statistical Mechanics and its Applications 294, 503 (2001) Google Scholar
  26. A. Blank, S. Solomon, Physica A 287, 279 (2000) Google Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.The Racah Institute of Physics, The Hebrew University of JerusalemJerusalemIsrael
  2. 2.Institute for Scientific InterchangeTurinItaly

Personalised recommendations