# Evolutionary dynamics with game transitions

## TL;DR

This paper investigates how dynamic changes in the environment, modeled as game transitions, influence the evolution of cooperation in structured populations, revealing that certain transition rules can promote prosocial behavior.

## Contribution

It introduces a model of evolutionary dynamics with game transitions and derives a simple rule showing how environment changes can favor cooperation.

## Key findings

- Weak selection favors cooperation if benefit-to-cost ratio exceeds a threshold involving game transition effects.
- Game transitions can promote cooperation even when individual games do not favor it.
- Small variations in game types can significantly enhance cooperative behavior.

## Abstract

The environment has a strong influence on a population's evolutionary dynamics. Driven by both intrinsic and external factors, the environment is subject to continual change in nature. To capture an ever-changing environment, we consider a model of evolutionary dynamics with game transitions, where individuals' behaviors together with the games they play in one time step influence the games to be played next time step. Within this model, we study the evolution of cooperation in structured populations and find a simple rule: weak selection favors cooperation over defection if the ratio of the benefit provided by an altruistic behavior, $b$, to the corresponding cost, $c$, exceeds $k-k'$, where $k$ is the average number of neighbors of an individual and $k'$ captures the effects of the game transitions. Even if cooperation cannot be favored in each individual game, allowing for a transition to a relatively valuable game after mutual cooperation and to a less valuable game after defection can result in a favorable outcome for cooperation. In particular, small variations in different games being played can promote cooperation markedly. Our results suggest that simple game transitions can serve as a mechanism for supporting prosocial behaviors in highly-connected populations.