Uncertainty, Information, Decision Making

Summary

^*In this chapter, we study how information can be incorporated as a variable in various decision models. In a decision model with uncertainty, it is natural to model information by sub-σ-fields of a probability space which represents the set of all possible states of the “world”. For this reason we topologize the set of sub-σ-fields with two topologies, using tools from probability theory and functional analysis. Then we examine the “ex-post view” and the “ex-ante view”. In both cases, we prove continuous dependence of the model on the information variable. Then we introduce a third mode of convergence of the information variable and we study prediction sequences. Finally we study games with incomplete information or unbounded cost and general state space.