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Małgorzata Fic1, Frank Bastian2, Jacek Miȩkisz3

  • 1Department of Theoretical Biology, Max Planck Institute for Evolutionary Biology, August-Thienemann-Str. 2, Ploen, 24306, Germany; Center for Computational and Theoretical Biology, University of Wuerzburg, Klara-Oppenheimer-Weg 32, Wuerzburg, 97074, Germany.

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Introducing time delays in evolutionary game theory models is complex. This research proposes a simpler compartment-based model that accurately captures strategy-dependent delays, showing they can harm affected strategies.

Keywords:
Bifurcation analysisDelay differential equationsEvolutionary game theoryStationary statesTime delays

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Area of Science:

  • Evolutionary Game Theory
  • Mathematical Biology
  • Computational Science

Background:

  • Real-world processes often involve time delays between actions and reactions, a factor frequently overlooked in standard modeling.
  • Incorporating explicit time delays into models significantly increases complexity, making analysis and computation challenging.

Purpose of the Study:

  • To propose a simplified, compartment-based model for evolutionary game theory that incorporates time delays.
  • To analyze the impact of strategy-dependent time delays on game dynamics, specifically focusing on parent-offspring interactions.

Main Methods:

  • Development of a compartment-based model that integrates time delays into evolutionary game theory.
  • Analysis of classic games including Stag-Hunt, Snowdrift, and the Prisoner's Dilemma under the influence of strategy-dependent delays.

Main Results:

  • The proposed model yields results comparable to those with explicit delays but remains simpler to analyze.
  • Strategy-dependent time delays were found to be detrimental to the strategies experiencing these delays.
  • The inclusion of delays can alter the effective games played within the population.

Conclusions:

  • Compartment-based models offer a tractable approach to incorporating time delays in evolutionary game theory.
  • Strategy-dependent temporal dynamics are crucial and can significantly impact evolutionary outcomes.
  • Accurate modeling of systems necessitates the consideration of their inherent temporal aspects.