We introduce new notions of bargaining set for mixed economies which rest on the idea of generalized coalitions (Aubin1979) to define objections and counter-objections. We show that the bargaining set defined through generalized coalitions coincides with competitive allocations under assumptions which are weak and natural in the mixed market literature. As a further result, we identify some additional properties that a generalized coalition must satisfy to object an allocation.

We give another proof for Kluvanek and Knowles’ characterization of Liapounoff measures [KLUVANEK, I.—KNOWLES, G.:

On a Boolean algebra we consider the topology u induced by a finitely additive measure µ with values in a locally convex space and formulate a condition on u that is sufficient to guarantee the convexity and weak compactness of the range of µ. This resultà la Lyapunov extends those obtained in (Khan, Sagara 2013) to the finitely additive setting through a more direct and less involved proof. We will then give an economical interpretation of the topology u in the framework of coalitional large economies to tackle the problem of measuring the bargaining power of coalitions when the commodity space is infinite dimensional and locally convex. We will show that our condition on u plays the role of the "many more agents than commodities"condition introduced by Rustichini and Yannelis in (1991). As a consequence of the convexity theorem, we will obtain two straight generalizations of Schmeidler's and Vind's Theorems on the veto power of coalitions of arbitrary economic weight.

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