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Periodic orbits in deterministic discrete-time evolutionary game dynamics: An information-theoretic perspective.

Sayak Bhattacharjee1, Vikash Kumar Dubey1, Archan Mukhopadhyay2

  • 1Department of Physics, Indian Institute of Technology Kanpur, Uttar Pradesh 208016, India.

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This study introduces the "information stable orbit" as a novel game-theoretic concept to interpret nonconvergent evolutionary dynamics. It generalizes the evolutionarily stable strategy, offering new insights into population state evolution.

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Area of Science:

  • Evolutionary Game Theory
  • Information Theory
  • Population Dynamics

Background:

  • Nonconvergent evolution is a known phenomenon in ecological and evolutionary contexts.
  • Existing evolutionary game theory lacks sufficient game-theoretic interpretations for these nonconvergent outcomes.

Purpose of the Study:

  • To develop a game-theoretic interpretation for periodic orbits in evolutionary game dynamics.
  • To generalize the concept of the evolutionarily stable strategy (ESS).

Main Methods:

  • Utilized the information-theoretic concept of relative entropy.
  • Constructed a game-theoretic interpretation for deterministic discrete-time evolutionary game dynamics.
  • Focused primarily on the two-player, two-strategy case.

Main Results:

  • Introduced and defined the
  • information stable orbit
  • as a generalization of the evolutionarily stable strategy.
  • Demonstrated that the information stable orbit captures the core idea of ESS by comparing payoffs against evolving mutants.
  • Established a connection between the information stable orbit and the dynamical stability of periodic orbits.

Conclusions:

  • The information stable orbit provides a novel framework for understanding nonconvergent evolutionary dynamics.
  • This concept offers a consistent generalization of the evolutionarily stable strategy.
  • The study bridges information theory and evolutionary game theory to explain complex population dynamics.