Fixation times in evolutionary games with the Moran and Fermi processes

Area of Science:

• Evolutionary game theory
• Mathematical modeling of social behavior
• Population dynamics

Background:

• Standard Moran and Fermi processes are foundational models in evolutionary game theory.
• Understanding cooperation and defection dynamics is crucial for social evolution.
• Mixed update mechanisms can offer a more realistic representation of population interactions.

Purpose of the Study:

• To investigate the fixation times of cooperation and defection in a novel mixed Moran-Fermi process.
• To analyze how information acquisition and payoff differences influence evolutionary outcomes.
• To provide a theoretical framework for understanding mixed strategy dynamics.

Main Methods:

• Development of a mixed process combining Moran and Fermi update rules.
• Derivation of balance equations for conditional and unconditional fixation times.
• Numerical analysis and simulations to validate theoretical findings.

Main Results:

• Expectation values of conditional fixation times for a single co-operator are lower than in standard processes.
• Co-operator fixation time under Moran rule exceeds Fermi rule at low selection intensity.
• Increased information acquisition by co-operators significantly reduces unconditional fixation time.
• Larger payoff differentials between strategies decrease unconditional fixation time.

Conclusions:

• The mixed Moran-Fermi process offers new insights into evolutionary dynamics.
• Information availability and payoff structure are key determinants of cooperative strategy success.
• This model provides a nuanced understanding of cooperation in structured populations.