Evolutionary Dynamics of Variable Games in Structured Populations

TL;DR

This paper introduces a variable game framework in structured populations, deriving conditions for cooperation, identifying optimal game distributions, and validating findings through simulations to better understand cooperative evolution.

Contribution

It develops a theoretical framework for dynamic game interactions in structured populations and determines optimal conditions for fostering cooperation.

Findings

Derived conditions under which cooperation is favored by natural selection.

Identified optimal game distributions that promote cooperation.

Validated theoretical predictions with numerical simulations.

Abstract

The game interactions among individuals in nature are often uncertain and dynamically evolving, significantly influencing the persistence of cooperation. However, it remains a formidable challenge to effectively characterize these dynamic properties in structured populations, derive theoretical conditions for cooperation, and identify the optimal game distribution for promoting cooperation. To address these issues, we propose the variable game framework in a structured population, where the game interactions between different individuals change over time. By means of the Markov chain and the pair approximation method, we derive theoretical conditions under which cooperation is favored by natural selection and when it is favored over defection under weak selection. Furthermore, we respectively formulate and solve two optimization problems to determine the optimal game distribution that most effectively fosters the evolution of cooperation by maximizing the gradient of cooperation selection and minimizing the fitness difference between defectors and cooperators. The theoretical predictions regarding both the conditions for cooperation and optimal game distribution are further validated by numerical calculations and extensive Monte Carlo simulations. Our findings offer novel insights into the mechanisms driving cooperative behavior in complex systems and provide theoretical guidance for designing optimal game environments that facilitate the evolution of cooperation.