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Essays in the Economics of Information and Epistemology

  • Author(s): Fukuda, Satoshi
  • Advisor(s): Ahn, David S
  • et al.
Abstract

This dissertation consists of three chapters exploring the role that information plays in strategic situations. The first two chapters are devoted to modeling a decision maker's reasoning (knowledge, beliefs, and unawareness) about those of other decision makers in strategic environments. The third chapter, in turn, studies how information and such reasoning affect economic behaviors.

The first chapter, The Existence of Universal Knowledge Spaces, provides a formal framework which enables us to analyze players' interactive knowledge and beliefs in a strategic context with a number of desirable features. First, the framework can specify players' logical and introspective properties of knowledge as well as depth of their reasoning. In other words, the framework admits various forms of introspective and non-introspective knowledge as well as beliefs which may fail the truth axiom of knowledge. Second, the framework generalizes previous interactive knowledge and belief models. Especially, it proposes notions of common knowledge and common belief without assuming any property on individual knowledge and belief. The main result of the first chapter is to propose a canonical representation of players' knowledge and beliefs under this general framework. The canonical model is universal in the sense that it ''contains'' any other particular representation.

The second chapter, Representing Unawareness on State Spaces, examines notions of unawareness in terms of the lack of knowledge within the framework of a standard state space model. For example, if a notion of unawareness is defined as the two levels of the lack of knowledge, then a player is unaware of an event when she does not know it and she does not know that she does not know it. In this way, this chapter studies notions of unawareness by a layer of the lack of knowledge and by underlying properties of knowledge. The central questions of the chapter are as follows. When and how does a standard state space model have a sensible form of unawareness? How does unawareness relate to notions of ignorance and possibility? The results are as follows. First, any notion of unawareness reduces to the following two forms. A strong form of unawareness states that a player is unaware of an event when she is ignorant of the possibility that she knows it. A weak form of unawareness states that a player is unaware of an event when she is ignorant of the fact that she knows it. Second, if a player is unaware of an event, then she is ignorant of being unaware of it. Third, if a player faces an infinite number of objects of knowledge, then it is possible that she knows that there is an event of which she is unaware, while she cannot know that she is unaware of any particular event. Fourth, unawareness is not necessarily monotone in knowledgeability in the sense that getting more information can lead a player to becoming unaware of some event.

The third chapter, From Equals to Despots: The Dynamics of Repeated Decision Making in Partnerships with Private Information, is a joint work with Vinicius Carrasco and William Fuchs. It considers the optimal dynamic renegotiation-proof mechanism among a group of privately informed agents who repeatedly take a joint common action but who are unable to resort to side-payments. The chapter provides a general framework which accommodates as special cases committee decision and collective insurance problems. Thus, it formally connects these separate strands of literature. In such a collective decision-making situation, the players may be tempted to exaggerate their preferred actions in order to manipulate the group action. While the first-best values can never be exactly attained in an incentive compatible way, the cost of incentives approximately disappears as the players become patient. In the optimal mechanism, a player who has a ''strong'' preference shock can influence a current joint action at the cost of forgoing continuation utilities. Such intertemporal trade-off in the optimal mechanism leads to the variations in the players' decision rights in a way such that they increase in expectation over time

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