This dissertation contains three essays in game theory, focusing particularly on the issues of information, knowledge, and stability in complex interactions. It begins with an introductory overview.; Chapter 2 offers a general framework for analyzing complex economic and social environments. Specifically, I introduce new notions of a general system and a ϕ-stable set. By making use of Tarski's fixed point theorem, I then establish the existence of a ϕ-stable set. I further apply the proposed notions to game theory, e.g., rationalizability is derived from the largest ϕ-stable set.; Chapter 3 establishes epistemic foundations for the criterion of "stability." Specifically, in strategic games, achieving common knowledge of rationality (CKR) implies an internally ϕ-stable set that is contained in an externally ϕ-stable set and, moreover, whenever mutually known, a ϕ-stable set is implied by rationality alone. In the case of two-person games, achieving CKR implies a ϕ-stable set. In extensive games with perfect information, achieving CKR implies a unique ϕ-stable set. On the other hand, in both strategic and extensive games, any of the commonly known ϕ-stable sets implies CKR. Furthermore, any ϕ-stable set can be achieved in terms of CKR.; Chapter 4 presents a new solution concept of stable equilibrium in beliefs (SEB) by assuming it is common knowledge that players are uncertainty averse. By making use of an appealing criterion of "stability," an SEB is defined as a strategy profile supported by a stable belief system. It is shown that all SEBs constitute a unique stable belief system, and an SEB satisfies subgame perfectness; moreover, it is shown that the notion of SEB "refines" that of subgame perfect equilibrium in terms of path of play. Finally, we establish the epistemic foundation for the notion of SEB.
展开▼
