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We consider pure exchange economies with a finite number of private goods and the choice of non-Samuelsonian public goods. For this type of economies, [5] proposed the notion of cost share equilibrium with individual payments for public goods varying according to individual benefits. This situation arises naturally when a level of provision is interpreted as a whole configuration of public policies or when cost share functions are interpreted as voluntary contributions rather than predetermined tax systems (see [31]). We establish the equivalence of cost share equilibria with cooperative and non-cooperative game-theoretic solutions: 1. we characterize cost share equilibria as those allocations which cannot be improved upon by society; 2. we characterize cost share equilibria as the Nash equilibria of a game with two players. The cooperative solutions analyzed in the paper are defined via a contribution scheme which captures the fraction of the total cost of collective goods that each coalition of agents is expected to cover. [ABSTRACT FROM AUTHOR]