1. By construction, (W * , P * ) is rational;P * ) is strongly rational in the product model. The result follows from Theorem
2. Since s ? K i K j (E), we have W i (s)(t) ? K j (E|i s ), i.e., P j (W i (s)(t)|i s ) ? References Bacharach, Michael;Journal of Economic Theory,1985
3. Standard State-Space Models Preclude Unawareness;Eddie Dekel;Econometrica,1998