Most of real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of the parameters influencing their dynamics. While in the physical systems the random component is usually additive (e.g. molecules can absorb or emit spontaneously energy quanta), in biological, social, economic and financial systems the noise is mainly multiplicative . The special properties of multiplicative noise as opposed to the 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. In the present paper we study in some detail the difference between the emergence of cooperation in additive vs. multiplicative random environments. 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. In fact given a set of individuals that play independently and repeatedly a game where they can gain by a factor a>1 with probability p or loose by a factor b<1 with probability q=1-p, one can show that for a^p b^q < 1 < pa +q b the cooperation makes the difference between extinction and (thriving) survival. We study quantitatively the various implications of this observation and its applications in various contexts.
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.
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While in the physical systems the random component is usually additive (e.g. molecules can absorb or emit spontaneously energy quanta), in biological, social, economic and financial systems the noise is mainly multiplicative
These empirical systems are in many cases subject to noise of multiplicative nature
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In the present paper we study in some detail the difference between the emergence of cooperation in additive vs. multiplicative random environments.
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In fact given a set of individuals that play independently and repeatedly a game where they can gain by a factor a>1 with probability p or loose by a factor b<1 with probability q=1-p, one can show that for a^p b^q < 1 < pa +q b the cooperation makes the difference between extinction and (thriving) survival. We study quantitatively
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