Homework 6
1) Consider the following game that we have studied in class:
E
Out
In1
In2
(0;2)
I
F
A
F
(-1;-1) (3;-2)
A
(;-1) (2;1)
We have solved for the weak PBE for the case when >0 and 1=2/3 (the Incumbents
belief that shows that the Incumbent thinks th
Homework 2 Suggested Solutions
1) For this game, the prot function of the rst rm is q1 (
q1 q2 ) cq1 f . As noted in the exercise,
the presence of the xed costs does not aect the rm output if it decides to produce. So, the optimal
s
output is given by a u
Homework 3 Suggested Solutions
1) If you swim on the rst day, your expected payo, as calculated in the question is
c + 2(1
)
and does not depend on your friend actions. If you wait and the friend goes swimming, then he is
s
attacked with probability
and y
Homework 3
1) From Osborne (Exercise 114.4)
You and a friend are spending two days at the beach; you both enjoy swimming.
Each of you believes that with probability the water is infested with sharks. If
sharks are present, a swimmer will surely be attacke
Homework 2
1) From Osborne (Exercise 59.2)
Find the Nash equilibria of Cournots game when there are two firms, the inverse
demand function is given by p(q)=-q and the cost function of each firm i is given
by 0 if qi=0 and f+cqi if qi>0, where c>=0, f>0, a
Homework 1
1) From Osborne (Exercise 27.2)
Two people enter a bus. Two adjacent cramped seats are free. Each person must
decide whether to sit or stand. Sitting alone is more comfortable than sitting next
to the other person, which is more comfortable tha
Homework 5
1) From Osborne (Exercise 173.4) Army 1, of country 1, must decide whether to
attack army 2, of country 2, which is occupying an island between the two
countries. In the event of an attack, army 2 may fight, or retreat over a bridge to
its main
Homework 5 Suggested Solutions
1) With bridge intact, if the rst army attacks, the second army will retreat (not occupying the island
is preferred to ghting), and the rst army will get the island. If the rst army does not attack, it does
not get the islan
Homework 6 Suggested Solutions
1) Assume that there is a weak PBE in which
0
= 1. Then whatever the strategy of the Incumbent,
the Entrant will get positive payos from playing
In2 it will be a mixture of payos
> 0 and 2.
Therefore, playing
In2 is strict
Homework 4 Suggested Solutions
1) First, consider the action of rm T. It knows its own state with certainty, so it will accept a bid if
and only if y is greater or equal to x.
Now, when rm A bids y (assume y is an integer), it knows that only rms with typ
Homework 1 Suggested Solutions
Sit
2;2
1) a) Sit
Stand
3;0
Stand 0;3
0;0
This game is not the Prisoner Dilemma since playing dominant strategies does not result in a Paretos
dominated outcome. The unique Nash equilibrium of this game is (Sit;Sit);
Sit
2;2