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Algorithms, complexity, and the sciences.

Christos Papadimitriou1

  • 1Simons Institute for the Theory of Computing, University of California, Berkeley, CA 94720 christos@berkeley.edu.

Proceedings of the National Academy of Sciences of the United States of America
|October 29, 2014
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Summary
This summary is machine-generated.

This study explores computational complexity, linking algorithms and complexity classes P and NP to phenomena in economics and evolution. It reveals algorithmic interpretations for Nash equilibrium and allele frequency evolution.

Keywords:
complexity of equilibrialens of computationmultiplicative weights update

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Area of Science:

  • Computational Complexity Theory
  • Evolutionary Biology
  • Game Theory
  • Economics

Background:

  • Algorithms and computational complexity are central to the information technology revolution.
  • Fundamental complexity classes P (polynomial time) and NP (nondeterministic polynomial time) define problem-solving limits.
  • Understanding complexity is crucial for diverse scientific fields.

Purpose of the Study:

  • To introduce basic concepts of algorithms and complexity classes P and NP.
  • To explore complexity classes between P and NP relevant to social and life sciences.
  • To provide algorithmic interpretations for phenomena in economics and evolutionary genetics.

Main Methods:

  • Introduction to algorithms, complexity, and the P vs. NP problem.
  • Focus on complexity classes capturing phenomena in economics (Nash equilibrium) and population genetics.
  • Application of the multiplicative weights update (MWU) algorithm to model allele frequency evolution.

Main Results:

  • Nash equilibrium may be less universally applicable than previously assumed.
  • Gene interactions might maintain genetic variation longer than single-allele selection.
  • The MWU algorithm provides an interpretation for allele frequency evolution, maximizing a fitness-entropy combination.

Conclusions:

  • Algorithmic insights offer new perspectives on economic equilibria and evolutionary processes.
  • The universality of Nash equilibrium is questioned.
  • Algorithmic interpretations of evolution may explain the maintenance of genetic variation.