In this dissertation, I investigate the core with asymmetric information (Chapters 2 and 3) and the Shapely value with externalities (Chapter 4). In Chapter 2 (jointly with Professor Roberto Serrano), we investigate to what extent the core convergence results hold for core notions with asymmetric information. We concentrate on the core with respect to equilibrium blocking, a core notion in which information is transmitted endogenously within coalitions, as blocking can be understood as an equilibrium of a communication mechanism used by players in coalitions. We identify conditions under which asymmetric information remains as an externality and non-market outcomes stay in the core, as well as those for the core to converge to the set of incentive compatible ex-post Walrasian allocations. In Chapter 3, I investigate the non-emptiness of the incentive compatible coarse core. I show that the incentive compatible coarse core is non-empty in quasilinear economies, if agents are informationally small and the strict core in each state is non-empty. This result means that in quasilinear economies, the non-emptiness result in Vohra (1999) is robust to the relaxation of non-exclusive information. In Chapter 4, I analyze a situation where several players entail cooperation in the presence of externalities by using games in partition function form. I concentrate on the axioms of anonymity, monotonicity, and weak dummy on a restriction operator, which is defined in Dutta, Ehlers and Kar (2008) for the potential approach. I connect the Shapley value of the associated characteristic function constructed from a restriction operator with values of games in partition function form proposed in previous literature.
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