Incomplete Information and Rational Choice:Continous Lexicographic Choices, Preference Manipulation, Error-Induced Certainty Equivalents and Information Gathering Algorithms

Resumen

The first chapter provides a brief review of the main concepts and nota tions employed throughout the dissertation. In the second chapter, we construct a model where choices are defined by preference relations induced by incomplete information on a set of com modities, whose elements are given by finite dimensional vectors of charac teristics. Induced lexicographic choices are shown to follow from continuous preferences and to be representable by continuous utility functions that are both additive and lexicographic. The third chapter provides an innovative set-theoretical approach to the problem of strategic information transmission. A choice set of either finite or infinite cardinality formed by multidimensional objects without any topolog ical structure is introduced. The information provided by a sender is encoded in a multifunction that forces the decision maker to choose according to the preference relation induced by the encoded information. The fourth and fifth chapters provide two alternative formal justifications for the existence of subjective random components intrinsic to the outcome evaluation process of agents and explicitly assumed in the stochastic choice literature. Contrary to the standard literature, which requires irrational preferences to generate errors through the choice process, adjustment choice errors arise in a natural way within both our settings, and their existence follows directly from the disconnectedness of the range of the utility functions. Finally, in the last chapter, we define explicitly the sequential information gathering structure of a rational decision maker. In doing so, we derive endogenous optimal decision threshold values as direct functions of the utility and probability densities inherent to the decision maker. We analyze in detail the case where the decision process is based on the possibility of collecting two pieces of information. Our results, and the logical structure behind them, can be extended to construct a general rational information gathering algorithm.