NAME_______________________________________________________________
FE461 Practice Problem
Fourth Problem Set
Due March 27th
1. (25 points) Let the inverse demand function in an industry be P(Q) = 40 – 3Q. There are
two firms in this industry, firm 1 faces costs given by: C(q1) = 5 + 10q1,and firm 2 faces
costs given by C(q2) = 5 + 13q2.
a) (15 points) Assuming Cournot competition, find the profits for each firm. (Note: the
firms face asymmetric costs.)
b) (10 points) Assuming Bertand competition, find the profits for each firm.
2. (20 points) Consider a Stackleberg game of quantity competition between two firms.
Firm 1 is the leader and firm 2 is the follower. Market demand is described by the inverse
demand function P = 1,000 – 4Q. Each firm has a constant unit cost of production equal
to 40. Solve for the Nash Equilibrium quantities for each firm.
3. (25 points) Suppose that firm 1 can choose to produce either good A or good B or both
goods or nothing. Firm 2, on the other hand, can produce only good C or nothing.
Firms’ profits correspond d to each possible scenario of goods for sale are described in
the following table:
Product Selection
Firm 1’s profit
Firm 2’s profit
A
20
0
A,B
18
0
A,B,C
2
-2
B,C
-3
-3
C
0
10
A,C
9
8
B
11
0
a) (10 points) Set up the normal form game for when the two firms move simultaneously.
What is the Nash Equilibrium (equilibria)?
b) (5 points) Now suppose that firm 1 can commit to its product choice before firm 2. Draw
the extensive form of this game and identify the Subgame Perfect Nash equilibrium
(SPE). Compare your answer to (a) and explain.
c) (10 points) The game is like the one in (b) only now suppose firm 1 can reverse its
decision after observing firm 2’s choice and this possibility is common knowledge. Does
this affect the game? If so, explain the new outcome? If not, explain why not.
4. (25 points) In a Centipede game suppose there are 2 players, player 1 moves first and
player 2 moves second and each player makes only one decision. The game begins with
$1 on the table. Player 1 can either “take” the $1 or “wait”; if player 1 chooses “take” the
game ends and player 1 earns $1 and player 2 earns $0. If player 1 chooses “wait” the
money quadruples (the $1 is now worth $4) and now player 2 can decide to “keep” or
“split”. If player 2 chooses “keep” player 2 earns $4 and player 1 earns $0; if player 2
chooses “split” both players earn $2.
a) (5 points) Draw the extensive form of this game.
b) (5 points) What is the subgame perfect equilibrium?
c) (15 points) Now suppose that Centipede has 3 three moves. First player 1 moves and
chooses “keep” or “wait”; then player 2 chooses “keep” or “wait”. If player 2 now
chooses “wait” the money quadruples again (so the $4 is now worth $16). Then player 1
moves last and can decided to “keep” (player 1 earns $16 and player 2 earns $0) or
“split” (both players earn $8). Draw the extensive form game and find the subgame
perfect equilibrium.