We address two issues that puzzled moral and socio-economic thinking since antiquity. The first of the puzzles is the emergence and selection fitness of altruist behavior in a world of self-reproducing individuals (or capital,etc.; memes in general). The second is the sustainability of growth and the survival in a stochastic world where along with large gains individuals incur often very large and even total losses. We show that the solution for each of these puzzles lies within the other one. It is known that in a multiplicative random process even if in the mathematical evaluation of the expected gain the wins overwhelm the losses, one is likely to be faced with extinction.For example if the probability of a total loss event is arbitrarily small but finite, the measure of histories with non-vanishing gains approaches 0 for asymptotic times >. Thus the optimistic theoretical expectation is dominated by event chains whose probability is too small to happen in reality. We find that in those situations, there is a way to insure self survival. The individuals can insure continuous, unlimited growth by sharing their gains/losses after each step of the random process. We compute the minimal necessary sharing group size Ncrit . Usually, in order to make "sharing" a stable profitable strategy, one has to introduce a credible punishment (/reward) mechanism that can be trusted by the individuals. However, such coercion is incompatible with the concept of real altruism. In a group of Ncrit individuals , defection by one individual leads automatically, thus credibly, to the ruin of the entire group (including the defector) . Consequently sharing becomes the only stable survivalstrategy without the need of any additional enforcing mechanism. This implies the survival and thriving of "altruistic genes" for very long evolutionary periods .
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 .
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We address two issues that puzzled moral and socio-economic thinking since antiquity. The first of the puzzles is the emergence and selection fitness of altruist behavior in a world of self-reproducing individuals (or capital,etc.; memes in general). The second is the sustainability of growth and the survival in a stochastic world where along with large gains individuals incur often very large and even total losses. We show that the solution for each of these puzzles lies within the other one. It is known that in a multiplicative random process even if in the mathematical evaluation of the expected gain the wins overwhelm the losses, one is likely to be faced with extinction.For example if the probability of a total loss event is arbitrarily small but finite,
Most of real life systems have a random component: the multitude of endogenous and exogenous factors influencing them result in stochastic fluctuations of
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measure of histories with non-vanishing gains approaches 0 for asymptotic times >. Thus the optimistic theoretical expectation is dominated by event chains whose probability is too small to happen in reality. We find that in those situations, there is a way to insure self survival. The individuals can insure continuous, unlimited growth by sharing their gains/losses after each step of the random process. We compute the minimal necessary sharing group size Ncrit . Usually, in order to make "sharing" a stable profitable strategy, one has to introduce a credible punishment (/reward) mechanism that can be trusted by the individuals. However, such coercion is incompatible with the concept of real altruism. In a group of Ncrit individuals , defection by one individual leads automatically, thus credibly, to the ruin of the entire group (including the defector) . Consequently sharing becomes the only stable survivalstrategy without the need of any additional enforcing mechanism. This implies the survival and thriving of "altruistic genes" for very long evolutionary periods
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