Before revision:  For any benefit-cost ratio above 1, the stable stationary concentrations of agents pass through four regimes as the baseline death rate p increases : (i) defection only, (ii) coexistence, (iii) cooperation only, (iv) extinction.
After revision:  For any benefit-cost ratio above 1, the extinction transition of the contact process splits into a set of nonequilibrium transitions between four regimes when increasing the baseline death rate p increases : (i) defection only, (ii) coexistence, (iii) cooperation only, (iv) extinction.