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An Introduction to Decision Theory

Martin Peterson

Chapter 1

Introduction - all with Video Answers

Educators

Chapter Questions

02:10

Problem 1

Explain the difference between:
(a) Decisions under risk and ignorance
(b) Social choices and decisions made by individuals
(d) Games and all other types of decisions discussed here

Patina Herring
Patina Herring
Numerade Educator
05:52

Problem 2

Consider the following situations:
(a) Charles Lindbergh was the first man to fly single-handed across the Atlantic in 1927. Did he make a decision under risk or ignorance as he departed New York and set off eastwards?
(b) You are thinking about flying to Paris next week. Are you making a decision under risk or ignorance?

Bobby Barnes
Bobby Barnes
University of North Texas
01:52

Problem 3

Consider the four lotteries below. Exactly one winning ticket will be drawn in each lottery.
$$
\begin{array}{llll}
\hline & \text { Ticket no. 1 } & \text { Ticket no. 2-20 } & \text { Ticket no. 21-100 } \\
\hline \text { Lottery A } & \text { \$2 million } & \text { \$2 million } & \text { \$2 million } \\
\text { Lottery B } & \text { \$0 } & \text { \$15 million } & \text { \$2 million } \\
\text { Lottery C } & \text { \$2 million } & \text { \$2 million } & \text { \$0 } \\
\text { Lottery D } & \text { \$0 } & \text { \$15 million } & \$ 0 \\
\hline
\end{array}
$$
(a) Make intuitive comparisons between lottery A and B, and between $\mathrm{C}$ and $\mathrm{D}$, without performing any calculations. Do you prefer A or B? C or D?
(b) Now calculate the expected (monetary) value of each lottery. Which lottery has the highest expected monetary value, A or B? C or D?
(c) Did these calculations make you change your mind? If so, why? (This is a version of Allais' paradox, which we will discuss in more detail in Chapter 4.)

James Kiss
James Kiss
Numerade Educator

Problem 4

Consider the following game, in which both you and your opponent have two alternatives to choose between. The first number in each box represents your payoff, whereas the second number represents your opponent's payoff. (Naturally, better payoffs are represented by higher numbers.)
$$
\begin{array}{llll}
\hline & & {\text { Your Opponent }} \\
& & \text { Alt 1 } & \text { Alt 2 } \\
\hline \text { You } & \text { Alt 1 } & 1,1 & 0,3 \\
& \text { Alt 2 } & 3,0 & 2,2 \\
\hline
\end{array}
$$
(a) What do you expect your opponent to do?
(b) What will you do?
(c) Try to explain why this game is of less theoretical interest than the stag hunt game.

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Problem 5

Briefly summarise the major events in the history of decision theory.

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