On the Economics of Information: Three Essays
Lee, Jong Jae
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In this dissertation, we study whether individuals with differing interests are able to achieve a socially efficient outcome in the presence of incomplete information about the others. Unlike the case of complete information, an individual's decision may reveal his private information, thereby impinging on the others' decisions. This signaling aspect of one's decision would force a decision maker to take account of what others would come to know about his private information. Studying this feature leads us to a rigorous examination, first of all, of how the notion of information ought to be understood and thus to be mathematically formulated; and secondly, of how this signaling aspect reduces the range of achievable efficient decision rules relative to the case of complete information. In the first chapter titled ``Formalization of Information: Knowledge and Belief'', we engage in the first task by studying the issue Billingsley (1995) and Dubra and Echenique (2004) raise about the use of sigma-algebra to model information. They provide an example to show that the formalization of information by sigma-algebras and by partitions need not be equivalent. Although Herves-Beloso and Monteiro (2012) provide a method to generate a sigma-algebra from a partition and another method for going in the opposite direction, we show that their two methods are in fact based on two different notions of information: (i) information as belief, (ii) information as knowledge. If information is conceived to allow for falsehood, case (i) above, the equivalence between $\sigma$-algebras and partitions holds after applying the notion of posterior-completion suggested by Brandenburger and Dekel (1987). If information is conceived not to allow for falsehood, case (ii) above, the equivalence holds only for measurable partitions and countably-generated sigma-algebras. In the second chapter titled ``Common Knowledge and Efficiency with Incomplete Information", we engage in the second task. Holmstrom an Myerson (1983) show that we need only check for efficiency on common knowledge events to determine that an incentive compatible decision rule is efficient. By a sharper notion of common knowledge, based on the notion of posterior-completion described in the first chapter, we show that we need only check for efficiency in a strict subset of common knowledge events known as self-evident events and furthermore, that this is the minimal class of events that one needs to check. In the third chapter titled ``Mediator Selection in International Conflict: Bias, Effectiveness, and Incidence", we adapt the question of achieving efficiency to the context of international conflicts and mediation. As war incurs a cost, an efficient outcome is thus a peaceful one in this context. We allow for disputants to make a joint decision whether to accept a potentially biased mediator who would communicate with them and propose a decision rule on their behalf. This extends the mechanism design problem of Horner et al (2015) to allow for mediator bias and its endogenous determination. Our main finding is that both disputants would accept a biased mediator if war is highly likely to occur in a conflict and the mediator's bias is moderate. More importantly, once a mediator has been accepted, the probability of attaining peace is independent of the intensity of her bias: because war is inefficient, the interest of the mediator's favored disputant is best served by promoting peace.