Nonlinear eco-evolutionary games with global environmental fluctuations and local environmental feedbacks
Fig 3
Phase plane dynamics of local game-environment (x − rc) evolution with N = 4, α = 1.5, β = 3.5, θ = 2, rd = 1.
We set w = 0.8, 1, 1.2 to describe the scenarios of discounting, linear, and synergy PGG in each column, and the corresponding ϵ* are 0.29, 0.44, 1.06, respectively. We therefore choose ϵ = 0.09, 0.24, 0.86 for the first row such that ϵ < ϵ*, and ϵ = 0.79, 0.94, 1.56 for the third row such that ϵ > ϵ*. The blue, pink and gray areas represent the basin of attraction of different fixed points and (
), respectively. The stable coexistence of cooperators and defectors only occurs when ϵ > ϵ* (the third row), as predicted theoretically, while a synergistically enhanced global environment significantly promotes the emergence of full cooperation (the third column).