Reference no: EM131253526

The Anscombe and Aumann derivation of subjective expected utility relies on the set of states of nature S being finite. How would we extend it to infinite state spaces? This problem takes you (step by step) through one extension that, essentially, adapts the original proof. There is a lot of setup and notation involved, so if you tackle this, please be patient. First, we provide a setup. Begin with an arbitrary state space S and an arbitrary prize space X. As in the text, let Π be the space of simple probability distributions on X. The setup also involves an algebra of subsets of S, denoted A; an algebra ofsubsets is a set ofsubsets such that (1) S ∈ A (2) if A ∈ A , then the complement of A, denoted A C, is also ∈A and (3) if A, B ∈ S then A ∩ B ∈ A (If you've never worked with this concept before, you might want to prove: If A has properties (1) through (3), then A is also closed under unions.) We can analyze the motion in each coordinate direction independently,
integrating the acceleration to determine the velocity and then integrating the velocity to determine the position.