Chapter 3
Exercise 3.11.1
In this case it is clear that a lot of information was revealed.
1
Chapter 3
Exercise 3.11.2
Now the Mad Hatter always has another strategy 0 (denoting the strategy of not
opening any boxes). If the Mad Hatter chooses 0 whenever
Chapter 5
Exercise 5.9.1
See figure 5.9.1
Figure 5.9.1
1
Chapter 5
Exercise 5.9.2
The successive elimination proceeds as follows. Step 1: d6 > d10 for player I. Step
2: d7 > d9 for player II. Step 3: d6 > d8 and d6 d0 for I. Step 4: d7 > d1
for II. Step 5
Chapter 1
Exercise 1.13.1
The payoff table is the following:
E
G
T
2
G
2
A
3
0
0
T
3
1
1
Thus, the strongly dominant strategy is T, for both players.
1
Chapter 1
Exercise 1.13.2
The outcome (hawk, hawk) is not Pareto efficient because the outcome (dove, d
Chapter 9
Exercise 9.10.1
Alice is violating the standard monotonicity assumption that she always prefers more
eggs over less eggs.
1
Chapter 9
Exercise 9.10.2
(a) 3;
(b) 2af ;
(c)
1
.
f a+2a
2
Chapter 9
Exercise 9.10.3
u (f, a) = (2af, a2 ), the equation
Chapter 6
Exercise 6.9.1
p=
1
, 0, 13 , 31
3
. To implement this strategy a player could throw a die and play the
first strategy if the result were 1 or 2, the third strategy if the result were 3 or 4 and
the fourth one otherwise.
1
Chapter 6
Exercise 6.9
Chapter 4
Exercise 4.11.1
Denote by A the expanded set of Pandoras alternatives. A maximum over the set A
is always at least as big as the maximum over any subset of A. For the second part
of the question notice that the set of alternatives, as perceived
Chapter 8
Exercise 8.9.1
(a) The strategic form can be represented by two tri-matrices. In every field, the
lower left hand payoff represents the payoff to player I and the upper right
hand entry is the payoff to II. The middle entry is the payoff of play
Chapter 6
Exercise 7.11.1
Take A B. If define b = max B.If b
/ A then a < b for every a A since a A
implies a B and b is the maximal element in B. If b A then max A = b since as
before all the other elements of A are smaller.
1
Chapter 6
Exercise 7.11.2
Chapter 10
Exercise 10.8.1
Where the isoprofit curves touch the gradients of the profits of Alice and Bob point
in the opposite directions. Thus, increasing one agents profit will necessarily decrease the others. The only candidates for Pareto-efficient o