


Part
I: Decision Problems
1
Introduction
............................................................................................................................
11
2
Outcomes and Preferences ...................................................................................................
15
2.1
Preference relations
2.2 Rational choice under
certainty
2.3 Why completeness and
transitivity?
2.4 Exercises
2.4.1 Exercises for Section 2.1:
Preference relations
2.4.2 Exercises for Section 2.2:
Rational choice under
certainty
2.5 Solutions to
Exercises
3
States and Acts
.......................................................................................................................
27
3.1
Uncertainty, states and acts
3.2 Dominance
3.3 MaxiMin
and LexiMin 34
3.3.1 MaxiMin
3.3.2 LexiMin
3.4 Regret: a first attempt
3.5 Exercises
3.5.1 Exercises for Section 3.1:
Uncertainty, states and acts
3.5.2
Exercises for Section 3.2: Dominance
3.5.3 Exercises for Section 3.3: MaxiMin and LexiMin
3.5.4 Exercises for Section 3.4:
Regret: a first attempt
3.6 Solutions to
Exercises
4
Decision Trees
.........................................................................................................................
43
4.1
Decision trees
4.2 Money lotteries and risk
neutrality
4.3 Backward induction
4.4 Beyond money lotteries and
risk
neutrality
4.5 Exercises
4.5.1 Exercises for Section 4.1:
Decision Trees
4.5.2 Exercises for Section 4.2:
Money lotteries and risk neutrality
4.5.3 Exercises for Section 4.3:
Backward induction
4.6 Solutions to
Exercises
Part
II: Uncertainty and Decision Making
5
Expected Utility Theory
........................................................................................................
71
5.1 Money lotteries and attitudes
to risk
5.2 Expected utility:
theorems
5.3 Expected utility: the axioms
5.4 Exercises
5.4.1 Exercises for Section 5.1:
Money lotteries and
attitudes to risk
5.4.2 Exercises for Section 5.2:
Expected utility theory
5.4.3 Exercises for Section 5.3:
Expected utility axioms
5.5 Solutions to
Exercises
6
Applications of Expected Utility
..........................................................................................
95
6.1 States and acts revisited
6.2 Decision trees revisited
6.3 Regret
6.4 The Hurwicz
index of pessimism
6.5 Exercises
6.5.1 Exercises for Section 6.1:
States and acts
revisited
6.5.2 Exercises for Section 6.2:
Decision trees revisited
6.5.3 Exercises for Section 6.3:
Regret
6.5.4 Exercises for Section 6.4:
The Hurwicz index of
pessimism
6.6 Solutions to
Exercises
7
Conditional Reasoning .........................................................................................................
123
7.1 Sets and probability: brief
review
7.1.1 Sets
7.1.2 Probability
7.2 Conditional thinking
7.2.1 The natural frequencies
approach
7.2.2 Conditional
probability
7.3 Simpson's paradox
7.3 Exercises
7.4.1 Exercises for Section 7.1:
Sets and probability
7.4.2 Exercises for Section 7.2:
Conditional thinking
7.5 Solutions to
Exercises
8
Information and Beliefs .......................................................................................................
151
8.1 Uncertainty and
information
8.2 Updating beliefs
8.3 Belief revision
8.4 Information and truth
8.5 Exercises
8.5.1 Exercises for Section 8.1:
Uncertainty and information
8.5.2 Exercises for Section 8.2:
Updating beliefs
8.5.3 Exercises for Section 8.3:
Belief revision
8.6 Solutions to
Exercises
9 The
Value of Information
...................................................................................................
169
9.1 When is information
potentially valuable?
9.2 The value of information when
outcomes are sums of
money
9.2.1 Perfect information and
risk
neutrality
9.2.2 Perfect information and
risk aversion
9.2.3 Imperfect
information
9.3 The general case
9.4 Different sources of
information
9.5 Exercises
9.5.1 Exercises for Section 9.1:
When is information potentially valuable?
9.5.2 Exercises for Section 9.2:
The value of
information when outcomes are sums of
money
9.5.3 Exercises for Section 9.3:
The general case
9.5.4 Exercises for Section 9.4:
Different sources of
information
9.6 Solutions to Exercises
Part
III: Thinking about Future Selves
10
Intertemporal Choice
.........................................................................................................
215
10.1 Introduction
10.2 Present value and
discounting
10.3 Exponential discounting
10.3.1 Time consistency
10.4 Hyperbolic discounting
10.4.1 Interpretation of the
parameter b
10.5 Dealing with time
inconsistency
10.6 Exercises
10.6.1 Exercises for Section
10.2:
Present value and discounting
10.6.2 Exercises for Section
10.3: Exponential
discounting
10.6.3 Exercises for Section
10.4: Hyperbolic discounting
10.6.4 Exercises for Section
10.5: Dealing with time
inconsistency
10.7 Solutions to
Exercises
Part
IV: Group Decision Making
11
Aggregation of Preferences
...............................................................................................
245
11.1 Social preference functions
11.2 Arrow’s
Impossibility Theorem
11.3 Illustration of the proof of
Arrow’s theorem
11.4 Application of
Arrow’s theorem to individual
choice
11.5 Exercises 1
11.5.1 Exercises for Section
11.1:
Social preference functions
11.5.2 Exercises for Section
11.2: Arrow’s impossibility
theorem
11.5.3 Exercises for Section
11.3: Illustration of the
proof of Arrow’s theorem
11.5.4 Exercises for Section
11.4: Application of
Arrow’s theorem to individual choice
11.6 Solutions to
Exercises
12
Misrepresentation of Preferences
...................................................................................
275
12.1 Social choice
functions
12.2 Strategic voting
12.3 The GibbardSatterthwaite
theorem
12.4 Illustration of the proof of
the GibbardSatterthwaite
theorem
12.5 Exercises
12.5.1 Exercises for Section
12.1: Social choice
functions
12.5.2 Exercises for Section
12.2: Strategic
voting
12.5.3 Exercises for Section
12.3: The GibbardSatterthwaite theorem
12.6 Solutions to Exercises .
Part V: Biases
in
Decision Making