Topics in Information Structures

Abstract

Economic analysis containing agents with incomplete information is common in many fields of economics, most notably Game Theory and Decision Theory. In these fields, information structures are typically represented by a state space of outcome-relevant variables, and each agent is endowed with a partition of the state space representing their information about the state of the world. This modeling implicitly assumes a great deal of logical sophistication on the part of agents in the model. For instance, agents can undertake introspection, and can never be mistaken. This thesis considers some effects of weakening various rationality assumptions on individuals' information processing capabilities. We allow agents to have much more general form of information structures in which agents may be mistaken, or potentially not understand modus ponens. These information structures are formalized by the knowledge operator, a function which takes each event into the set of states where the agent knows that the event has occurred. One consequence of this relaxation of assumptions is that the classical Aumann [1976] and Lewis [1969] definitions of common knowledge lose a range of desirable properties. A new definition of common knowledge is developed which reduces to the classical definitions when agents have sufficiently strong information processing capabilities, and retains many desirable properties even when agents lack these abilities. Information aggregation more generally is formalized, and a language for discussing knowledge aggregation is developed. Knowledge operators are used to develop a framework for the study of imprecise probabilities, the Behavioral Imprecise Probability. This new framework uses a standard probability function over the state space to capture Knightian risk, while the knowledge operator captures Knightian uncertainty, or ambiguity. Behavioral Imprecise Probability Models are systematically compared to existing frameworks of imprecise probability including the Multiple Prior Model of Gilboa and Schmeidler [1989], and totally monotone capacities, as in Dempster [1967], Shafer [1976], and Gilboa and Schmeidler [1994]. The second, much smaller, part of the thesis works on the Common Prior Assumption, or Harsanyi Consistency Problem Harsanyi [1967, 1968a,b]. This partreturns to using partitions to model information structures. Existing results of Rodrigues-Neto [2009] are generalised to allow for priors and posteriors without full support. Results from Hellwig [2013] are extended to remove geometric assumptions on the partitions of the agents. Show more