Problem 1:

(a) The demand function is P=12-Q. Since each firm will produce an output
of A/(n+1) wher n=2 we get for each firm an output of 4 units for a total
of 8 units. The corresponding price is P=4.

(b)If the two firms form a cartel and operate as a monopoly then the total
monopoly output is 6 units and each firm will produce 3 units each. The
price is P=6.

(c) Use the proof discussed in class. Suppose firm 2 maintains its output
at 3 units (the cartel quota) but firm 1 expands output to 4 units. The
resultant aggregate output is 7 units and the Price is 5. This yields
higher profit for Firm 1 than in the cartel situation.

Problem 2:

Top is dominated for Player 1 (by Center) and Left for Player 2 (by
Middle). 

Next Bottom dominates Center for Player 1 and Right dominates Middle for
Player 2.

So the dominant strategy Nas Equilibrium is (Bottom, Right)

Problem 3:

(a) This proof was (will be) worked out in class.

(b) To max profit set MR=MC.

for market 1, MR = 10 - 2q1. Setting this equal to 2 (MC) we get, q1 = 4
and for market 2 we get 20 - 2q2 = 2 which implies q2 = 9.

Problem 4:

(a) There are two Nash equilibria. (Top, Left) and (Bottom, Right)

(b) The sungame perfect Nash equilibrium is (Bottom. Right)

(c) the dominant strategy Nash equilibrium is (Bottom,Right)

Problem 5:

(a) Yes even if the game is played sequentially (Defect,Defect) is the
only subgame perfect equilbrium in the extensive form of this game.

(b) (Co-operate, Co-operate) can be sustained as an equilibrium in an
infinitely repeated version of this game for a discount factor (delta)
greater than 1/2.


Problem 6:

Rhonda should choose Wrestling 3/4 of the time and Bowling 1/4 of the
time.

Calvin should choose Wrestling 1/4 of the time and Bowling 3/4 of the
time.

Problem 7:

(a) Firm A would produce an output of 1/2. Firms 2 and 3 should each
produce an output of 1/6 each.

(b) Firms 1 and 2 should produce 1/3 each while Firm 3 produces 1/6.