Measure and cost dependent properties of information structures

Information structures capture how and when information is shared between the agents of a decentralized system. Traditionally, information structures are classified based on the data available at the agents. No assumptions on the probability measure or the cost function are imposed. This classification has helped in clarifying the conceptual difficulties of decentralized control. However, from a practical point of view, the classification based only on the data is restrictive as illustrated by the recent results on stochastically nested information structures. In this paper, we generalize the main idea of stochastically nested information structures to define extensions of classical and quasiclassical information structures that depend on the probability measure and the cost function. We show that the optimality results of classical and quasiclassical information structures extend to their stochastically nested counterparts.