This paper provides a formal framework within which to study cooperative behavior in the presence of incomplete information, and shows how far the known results in the static cooperative game theory can readily be applied to the proposed framework. The new concepts of Bayesian society, Bayesian strong equilibrium and Bayesian incentive compatible strong equilibrium are introduced and studied.

A closed cover version of Hazewinkel and van de Vel's theorem on the existence of-y-almost fixed points for set-valued functions and for real Hausdorff topological vector spaces is proved. Generalizations of well-known fixed point theorems of the Schauder-Tychonoff type are presented.

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In this paper, we first establish a coincidence theorem under the noncompact settings. Then we derive some fixed point theorems for a family of functions. We apply our fixed point theorem to study nonempty intersection problems for sets with convex sections and obtain a social equilibrium existence theorem. We also introduce a concept of a quasivariational inequalities and prove an existence result for a solution to such a system.