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Imitation dynamics with time delay.

Shi-Chang Wang1, Jie-Ru Yu2, Shun Kurokawa1

  • 1Key Lab of Animal Ecology and Conservation Biology, Institute of Zoology, Chinese Academy of Science, Beijing, China.

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|March 5, 2017
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Summary
This summary is machine-generated.

Introducing time delay into imitation dynamics reveals new evolutionary behaviors. A critical delay can stabilize periodic solutions in two-phenotype models and influence amplitude and period in rock-scissors-paper games.

Keywords:
Evolutionary game theoryImitation dynamicsPayoff matrixReplicator dynamicsTime delay

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Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Behavioral Dynamics

Background:

  • Classic imitation dynamics model strategy evolution based on payoff comparisons.
  • Time delays in decision-making can significantly alter evolutionary outcomes.

Purpose of the Study:

  • Investigate imitation dynamics incorporating a time delay effect.
  • Analyze the impact of time delays on equilibrium stability and population dynamics.

Main Methods:

  • Extended the classic imitation dynamics framework to include time-delayed strategy imitation.
  • Analyzed a two-phenotype model for equilibrium stability with time delay.
  • Employed numerical analysis for a three-phenotype (rock-scissors-paper) model with time delay.

Main Results:

  • In two-phenotype models, a stable interior equilibrium under no delay becomes a stable periodic solution beyond a critical time delay.
  • For the rock-scissors-paper model, increasing time delay leads to increased amplitude and period of stable periodic solutions.

Conclusions:

  • Time delays introduce complex dynamics, including stable oscillations, into evolutionary game models.
  • The findings provide insights into behavioral evolution influenced by delayed feedback mechanisms.