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Economics 327

Choice under uncertainty

1

Slide 1

✬

✫

✩

✪

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

z ∈ Z

¯

,

p(z ≤ ¯

z) ≤ q(z ≤ ¯

z)

Slide 2

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✫

✩

✪

Problems with stochastic dominance as a DT

z

p(z)

$

999 .01

$

1,000,000 .99

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Economics 327

Choice under uncertainty

2

Slide 3

✬

✫

✩

✪

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

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✫

✩

✪

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

. . .

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