Eur. Phys. J. B 73, 625-632 (2010)
https://doi.org/10.1140/epjb/e2010-00027-4

Cooperation evolution in random multiplicative environments

¹ The Racah Institute of Physics, The Hebrew University of Jerusalem, Edmond Safra Campus, Givat Ram, Jerusalem, 91905, Israel
² Institute for Scientific Interchange, via S. Severo 65, 10113 Turin, Italy

Corresponding author: gyaari@gmail.com

Received: 24 September 2009
Revised: 5 November 2009
Published online: 27 January 2010

Abstract

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.