Economics of Uncertainty and Information by Timothy Van Zandt

By Timothy Van Zandt

This ebook is ready uncertainty and knowledge in economics. Uncertainty and knowledge are inexorably associated. You face uncertainty if you happen to don't know anything concerning the global, reminiscent of the implications of your activities. which means you lack whole details. acquiring details then resolves this uncertainty

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He reasons that the guard’s reply tells him that the true state is in the event {L, C}. Applying Bayes’ Rule, π(L | { L, C}) = π(L)  = , π({L, C})  he calculated that the conditional probability of his execution is 1/2. Let’s check the information structure. By Larry’s reasoning, when the state is “Mo,” the guard says “Curly,” and Larry’s information is {L, C}. That is: I (M) = {L, C}. By the same reasoning, I (C) = {L, M}. Already we are in trouble. The information sets {L, C} and {L, M} are neither disjoint nor equal, and hence cannot be part of a partition.

Section 2 Bayes’ Theorem 47 We can calculate the probability of each event in {A  , . . , A m } conditional on each event in {E  , . . , E n }. For the example, we have π(A  | E  ) = / π(A  | E  ) = / π(A  | E  ) = / π(A  | E  ) = /. We can also calculate the probability of observing each information event. For the example, we have π(E  ) = / π(E  ) = /. 2. 2. Conditional probabilities for the example. ⎫ ⎪ ⎪ ⎪ ⎬ Unconditional 1/2 Smile 3/4 Likes me probabilities of ⎪ ⎪ ⎪ ⎭ information events 1/2 No smile 1/4 Likes me not 1/2 Likes me 1/2 ⎫ ⎪ ⎪ ⎪ ⎬ Conditional probabilities of ⎪ ⎪ ⎪ ⎭ payoff-rel.

6 Statewise dominance In the state-of-nature model, there is a criterion that is related to but stronger than first-order stochastic dominance. We call it statewise dominance, or simply dominance. An act x˜ dominates another act y˜ if it results in a better outcome in every state. We again write x y for x , y ∈ X if the sure outcome x is preferred to the sure outcome y. Then x˜ weakly dominates y˜ if x(s) ˜ y(s) ˜ for every s ∈ S. If also x(s) ˜ y(s) ˜ for some s ∈ S, then x˜ (strictly) dominates y.

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