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Learning increases growth and reduces inequality in shared noisy environments.

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Area of Science:

  • Complex Systems Dynamics
  • Information Theory
  • Socioeconomics

Background:

  • Stochastic multiplicative dynamics are prevalent in natural phenomena like population evolution and wealth distribution.
  • Population heterogeneity in stochastic growth rates is a key driver of long-term wealth inequality.
  • A general statistical theory explaining the origins of heterogeneity from agent-environment adaptation is lacking.

Purpose of the Study:

  • To derive population growth parameters from agent-environment interactions based on subjective signals.
  • To investigate the role of mutual information and Bayesian inference in optimizing growth rates.
  • To understand how learning processes affect growth rate disparities and inequality.

Main Methods:

  • Derivation of population growth parameters from agent-environment interactions.
  • Analysis of the relationship between mutual information and maximal average wealth-growth rates.
  • Modeling sequential Bayesian inference as an optimal strategy.

Main Results:

  • Average wealth-growth rates converge to maximal values under conditions of high mutual information between agent signals and the environment.
  • Sequential Bayesian inference is identified as the optimal strategy for achieving maximal growth rates.
  • Learning processes attenuate growth rate disparities when agents share the same statistical environment, reducing inequality.

Conclusions:

  • Formal properties of information underpin general growth dynamics in both social and biological systems.
  • Information acquisition and processing are critical for understanding cooperation and life history choices.
  • This framework offers insights into the impact of education and learning on socioeconomic and biological phenomena.