Cooperation Evolution in Random Multiplicative Environments

TL;DR

This paper explores how multiplicative noise in stochastic systems naturally promotes cooperation, contrasting with additive noise where cooperation requires specific incentives, and discusses various implications and applications of this phenomenon.

Contribution

It demonstrates that multiplicative noise inherently fosters cooperation more effectively than additive noise, offering new insights into stochastic dynamics and social behavior.

Findings

Multiplicative noise promotes cooperation naturally.

Additive noise requires incentives for cooperation.

Implications span various real-world contexts.

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.