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Evolution of populations with strategy-dependent time delays
1Institute of Applied Mathematics and Mechanics, University of Warsaw, Warsaw, Poland.
Physical Review. E
|February 19, 2021
Summary
Strategy-dependent time delays in evolutionary games create novel replicator dynamics. Stationary states now continuously depend on these delays, altering population equilibria and potentially leading to homogeneous strategies like cooperation.
Area of Science:
- Evolutionary Game Theory
- Dynamical Systems
- Population Dynamics
Background:
- Time delays are known to induce oscillations in dynamical systems.
- Standard replicator dynamics model population evolution without strategy-dependent time delays.
Purpose of the Study:
- To investigate the impact of strategy-dependent time delays on the equilibria of evolving populations.
- To introduce a novel replicator dynamics model that incorporates these delays.
Main Methods:
- Developing microscopic models of evolutionary games with strategy-dependent time delays.
- Analyzing the resulting new replicator dynamics.
Main Results:
- The novel dynamics exhibit stationary states that depend continuously on time delays.
- In games with a standard interior equilibrium, time delays can cause its disappearance or the emergence of new interior equilibria.
- In the Prisoner's Dilemma, specific delay conditions can lead to an unstable interior equilibrium, favoring convergence to a homogeneous cooperative state.
Conclusions:
- Strategy-dependent time delays introduce significant, previously unobserved behaviors in evolutionary game dynamics.
- These delays offer a new mechanism for controlling population-level strategy adoption and stability.
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