14.123 Microeconomic Theory III
Problem Set 1
The due date for this assignment is Thursday February 11.
1. Let P be the set of all lotteries p = (px , py , pz ) on a set C = cfw_x, y, z of consequences.
Below, you are given pairs of indierence sets on P .

Chapter 3
Decision Making under Uncertainty
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CHAPTER 3. DECISION MAKING UNDER UNCERTAINTY
the conditions such consistent beliefs impose on the preferences,
the elicitation of the beliefs from the preferences, and
the representation of the beliefs

Chapter 2
Decision Making under Risk
2.1
Consequences and Lotteries
Consider a nite set C of consequences. A lottery is a probability distribution p :
P
C [0, 1] on C, where cC p(c) = 1. The set of all lotteries is denoted by P . The
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CHAPTER 2. DECI

Chapter 6
Alternatives to Expected Utility
Theory
6.1
Allais Paradox and Weighted Utility
Imagine yourself choosing between the following two alternatives:
A Win 1 million dollar for sure.
B Win 5 million dollar with 10% chance, 1 million dollar with 89%,

Chapter 4
Attitudes Towards Risk
4.1
Theory
Take the set of alternatives as X = R which corresponds the wealth level of the decision
maker. The decision maker has an increasing von Neumann-Morgenstern utility func
tion u : R R, representing his preference

14.123 Microeconomic Theory III
Problem Set 3
The due date for this assignment is Thursday March 11
1. Lecture Notes; Chapter 6.4, Exercise 8.
2. Alice and Bob seek each other. Simultaneously, Alice puts eort sA and Bob puts eort
sB to search. The probabi

Chapter 1
Theory of Choice
1.1
Alternatives
Consider a set X of alternatives. Alternatives are mutually exclusive in the sense that
one cannot choose two distinct alternatives at the same time. Take also the set of feasible
alternatives exhaustive so that

Chapter 5
Stochastic Dominance
I will dene two notions of stochastic dominance:
1. First-order stochastic dominance: when a lottery F dominates G in the sense of
rst-order stochastic dominance, the decision maker prefers F to G regardless of
what u is, as

Chapter 8
Rationalizability
The denition of a game (N, S, u1 , . . . , un ) implicitly assumes that
1. the set of players is N , the set of available strategies to a player i is Si , and the
player i tries to maximize the expected value of ui : S R accord

Chapter 7
Preliminary Notions in Game
Theory
The games can be represented in two forms:
1. The normal (strategic) form,
2. The extensive form.
I rst describe these representations illustrate how one can go from one representation
to the other.
7.1
Normal

14.123 Microeconomic Theory III
Final Make Up Exam
(80 Minutes)
1. (30 points) This question assesses your understanding of expected utility theory.
(a) Show that there exists a preference relation on preferences that satises the in
dependence axiom but i