This paper develops a theoretical framework for four sustainability paradigms (weak sustainability, a-growth, de-growth, strong sustainability) within cooperative and non-cooperative scenarios, and includes changes in four values (a sense of responsibility to nature and future generations; aversion to inequality for current and future generations). The model assesses the feasibility of sustainability solutions for a shared environment as a function of specific value changes in each country by interpreting these value changes as support for environmental policies. The solutions are defined in terms of consumption, use of the environment, and welfare of representative individuals in each country; they are characterised by efficiency and equality at both intra- and inter-generational levels; they are checked for internal consistency and consistency with alternative approaches such as utilitarianism, egalitarianism (i.e., Arneson, Dworkin, Sen), and contractarianism. Theoretical insights are obtained by comparing contextual stability and relative effectiveness of the environment's use among countries in alternative scenarios. A case study of the Baltic Sea operationally suggests that the currently adopted strong sustainability (i.e., an ecosystem approach) in a non-cooperative scenario (i.e., countries attempt to maximize their own rather than overall welfare) is internally consistent, relatively efficient, and consistent with Dworkin egalitarianism. Agrowth was never feasible, but de-growth in which Denmark, Finland, Germany, and Sweden increase environmental protection would increase intra-generational equality; de-growth or weak sustainability in which Estonia, Latvia, Lithuania, Poland, and Russia increase environmental R&D would increase intra- and inter-generational equality; weak sustainability and de-growth consistent with Arneson and Dworkin egalitarianism would improve the environmental status.