Structural consistency and strategic independence in extensive games

In this note I provide a formulation of the joint principle of structural consistency and strategic independence, which is used to model players' expectations in finite extensive games. I compare updating systems of conjectures and conditional probability systems, showing that they represent equivalent formalizations of structural consistency. The notion of strategic independence cannot be adequately formalized by properties of updating systems of conjectures. However, it can be naturally translated in an intuitive stochastic independence property for conditional probability systems.