The Unification of Evolutionary Dynamics through the Bayesian Decay Factor in a Game on a Graph

Area of Science:

• Evolutionary Game Theory
• Mathematical Biology
• Network Science

Background:

• Evolutionary dynamics on graphs are complex, especially with strategic uncertainty.
• The Price theorem of selection is crucial for understanding replicator dynamics.
• Existing models often lack mechanisms to unify different evolutionary scenarios.

Purpose of the Study:

• To unify evolutionary dynamics on graphs under strategic uncertainty.
• To analyze the Price theorem of selection with a decaying Bayesian update.
• To establish equivalences between different evolutionary scenarios and identify conditions favoring cooperation.

Main Methods:

• Developed a decaying Bayesian update framework for evolutionary dynamics on graphs.
• Applied the Price theorem of selection with stratified interactions and composite strategy updates.
• Analyzed the conditions under which competition shifts to cooperation.

Main Results:

• Demonstrated an equivalence between mutation-driven cooperation shifts in well-mixed populations and strategy replication in Bayesian populations.
• Showed that cooperation can be favored irrespective of specific payoff levels.
• Identified specific conditions relating transition rates and selection strengths for this equivalence.

Conclusions:

• The unified framework simplifies the understanding of evolutionary dynamics under uncertainty.
• The findings offer new perspectives on the Price's equation applicability.
• Cooperation likelihood can be predicted by understanding selection dynamics rather than just payoffs.