Problem sets for Microeconomics II [110051-0471]

7 Game theory
Exercise 7.1. Firms M and N compete for a market and must independently decide
how much to advertise. Each can spend either $10 million or $20 million on
advertising. If the firms spend equal amounts, they split the $120 million market
equally. (For instance, if both choose to spend $20 million, each firm’s net profit
is 60 – 20 = $40 million.) If one firm spends $20 million and other $10 million, the
former claims two thirds of the market and the latter one-third.
a. If the firms act independently, what advertising level should each choose Explain.
Is a prisoner’s dilemma present
b. Could the firms profit by entering into an industry-wide agreement concerning
the extent of advertising Explain.
Exercise 7.2. A firm sells two goods in a market consisting of three types of consumers.
The table shows the values consumers place on the goods. The unit cost
of producing each good is $5.
Good
Consumers X Y
A 13 6
B 7 11
C 15 2
Find the optimal prices for (a) selling the goods separately, (b) pure bundling,
and (c) mixed bundling. Which pricing strategy is most profitable
Exercise 7.3. Find all Nash equilibriums in the game of two banks, whose management
considers selling to debtors their liabilities for the discounted price.
Bank II
S
NS
Bank I S 6,6 6,11
NS 11,6 6,6
Exercise 7.4. There are three payoff tables given.
a. Identify the equilibrium outcome(s) in each of the three payoff tables.
I. C 1 C 2
R 1 12,10 10,4
R 2 4,8 9,6
II. C 1 C 2
R 1 12,10 4,4
R 2 4,4 9,6
18
III. C 1 C 2
R 1 12,10 4,4
R 2 4,-100 9,6