Abstract
In this thesis, two most fundamental problems in economic theory, namely the existence and the optimality of Walrasian equilibrium, are studied. It is assumed that there is uncertainty about the realized state of nature in an economy and different agents may have different information. Such an economy is called an economy with asymmetric information. Considering a pure exchange symmetric information economy with finitely many states of nature, an atomless measure space of agents and a Banach lattice as the commodity space, it is shown that the private core and the set of Walrasian allocations coincide. The feasibility in this result is taken as free disposal. This optimality is known as the core-Walras equivalence theorem. When the feasibility is defined without free disposal, then it is shown that if a feasible allocation is not in the private core then it is privately blocked by a coalition of any given measure less than that of the grand coalition.
In addition to the above optimality, some other characterizations of Walrasian allocations by the veto power of the grand coalition are also established. One of them deals with robustly efficient allocations in a pure exchange mixed economy with asymmetric information whose commodity space is an ordered separable Banach space having an interior point in its positive cone. Other two characterizations are restricted to a discrete economy with a Banach lattice as the commodity space. First one claims that a feasible allocation is a Walrasian allocation if and only if it is Aubin non-dominated, whereas the other one is interpreted in terms of privately non-dominated allocations in suitable associated economies. The feasibility in all of these results is defined as free disposal.
In a pure exchange asymmetric information economy whose space of agents is a finite measure space, space of states of nature is a probability space with a complete measure, and commodity space is defined as the Euclidean space, the existence of a maximin rational expectations equilibrium is established.
