Slide 1

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A heading

One thing this example illustrates is how the article style option is good for printing slides two-up, for distribution to a seminar audience or class, or just for proofreading. Definition: p (weakly) first-order stochastically dominates q if for every z̄ ∈ Z,

p(z ≤ z̄) ≤ q(z ≤ z̄)

Slide 2

Problems with stochastic dominance as a DT

\begin{matrix}z & p(z) \\ $999 & .01 \\ $1,000,000 & .99 \end{matrix}  \begin{matrix}z & q(z) \\ $1,000 & 1 \end{matrix}

Slide 3

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Candidate Theory #3: Expected utility

Let Z be an arbitrary set of outcomes. Let u : Z → R be a utility representation of the DM’s preferences over the elements of Z as certain outcomes. (I.e., u(y) ≥ u(z) iff y ≥ z.)

Slide 4

Expected utility & the St. Petersburg Paradox

This can get around even St. Petersburg Paradox, because we don’t require that utility be linear in money:

Prize $2 $4 $8 $16 …
u(z) = log_{2}(z) 1 2 3 4 …
Prob. 1/2 1/4 1/8 1/16 …

Expected utility is ∑_{k=1}^{∞} k/2^{k} = 2, and so lottery gives same expected utility as getting $4 for sure.