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:  When cooperation has higher cost than benefit, cooperators disappear. Then the dynamics reduces to the contact process with defectors as the single particle type. Increasing the 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.