3
$\begingroup$

A wheel of fortune has outcomes $S=\left \{ 1000,100,50,20,0 \right \}$ as money prices. A consumer has the preferences

$$20\sim \left ( \frac{2}{100}\cdot1000 \oplus \frac{98}{100} \cdot 0 \right )$$ $$50\sim \left ( \frac{15}{100}\cdot1000 \oplus \frac{85}{100} \cdot 0 \right )$$ $$100\sim \left ( \frac{45}{100}\cdot1000 \oplus \frac{55}{100} \cdot 0 \right )$$

What does this notation mean? I figure that the direct sum is just showing that the percentage for winning $1000$ in the first equation is $2/100$ and $98/100$ for $0$. But what does the $20$ denote? Is this some utility and how would that be read with the indifference sign in front of it? Never seen the notation like this before.

Improve this question
$\endgroup$
5
$\begingroup$

$$ \left(\frac{2}{100} \cdot 1000 \oplus \frac{98}{100}\cdot 0\right) $$ is the lottery where you get $1000$ with probability $2/100$ and $0$ with probability $98/100$.

The expression $$ 20 \sim \left(\frac{2}{100} \cdot 1000 \oplus \frac{98}{100}\cdot 0\right) $$ usually says that the decision maker is indifferent (in terms of preferences) between taking the lottery and having $20$ for sure.

Improve this answer
$\endgroup$
9
  • $\begingroup$ So say that the consumer face 2 wheels. the first wheel the consumer wins $1000$ with probability $1/4$, $50$ with probability $1/4$ and $20$ for the rest. The second he wins $1000$ with probability $1/5$, $100$ with probability $1/4$ and nothing for the rest. How do I determine from the preference which he chooses from the $3$ equations? $\endgroup$
    – mathstudent23
    May 15 at 14:28
  • $\begingroup$ (just to take a look at the usage of the preferences) $\endgroup$
    – mathstudent23
    May 15 at 15:00
  • 1
    $\begingroup$ This should be a separate question. $\endgroup$
    – VARulle
    May 15 at 21:29
  • 1
    $\begingroup$ @mathstudent23 $\left ( \frac{1}{5}\cdot1000 \oplus \frac{1}{4} \cdot 100 \oplus \frac{11}{20} \cdot 0\right ) \sim$ $\left ( \frac{1}{5}\cdot1000 \oplus \frac{1}{4} \cdot \frac{45}{100}\cdot1000 \oplus \frac{1}{4}\cdot\frac{55}{100} \cdot 0 \oplus \frac{11}{20} \cdot 0\right )$ or something like that, which you can simplify $\endgroup$
    – Henry
    May 16 at 17:13
  • 1
    $\begingroup$ @mathstudent23 It can be simplified, but your fractions do not add up to $1$. Instead $\left(\frac{5}{16}\cdot1000 \oplus \frac{11}{16} \cdot 0\right)$ $\endgroup$
    – Henry
    May 17 at 0:10

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.