ME TUTORIAL 5 (GAME THEORY, OLIGOPOLY)
Q1. In Bakersville, there are two bakers, Andy and Cory. Andy's bread tastes just like Cory's;
nobody can tell the difference. Andy has constant marginal costs of $1 per loaf of bread. Cory
has constant marginal costs of $2 per loaf. Fixed costs are zero for both. The inverse demand
function for bread in Bakersville is
p(q)=6 −0.01q
,
where q is the total number of loaves sold per day.
a) Find Andy's Cournot reaction function.
b) Find Cory’s Cournot reaction function
c) Find the Cournot equilibrium quantities.
d) Find the profit for each baker
Q2. The inverse market demand curve for bean sprouts is given by
P(Y) = 100 −2Y ,
and the total cost function for any firm in the industry is given by TC(y)=4y.
a) If the bean-sprout industry were perfectly competitive, what would be the industry output
and the industry price?
b) Suppose that two Cournot firms operated in the market. What would be the reaction function
for each firm?
c) What would be the Cournot equilibrium in the above case?
d) What happens when the two firms decide to collude? What is the industry output and price
in event of collusion?
Q3. In a duopoly, the demand equations for both firms are as given:
q1=90-2p1+p2,
q2=90-2p2+p1
There are no variable costs associated with this industry (only a simplifying assumption; hard
to find in real life).
, a) What is the market equilibrium if the firms compete on the price front?
b) What is the market equilibrium if the firms compete in quantities?
c) Should they compete on prices or quantities?
Q4. Ann and Victoria are roommates. Each of them prefers a clean room to a dirty room, but
neither likes to clean the room. If both clean the room, they each get a utility of 5. If one
cleans and the other doesn't clean the room, the person who does the cleaning has a utility of
0, and the person who doesn't clean the room has a utility of 8. If neither cleans the room, the
room stays a mess and each has a utility of 1.
a) Is there a dominant strategy? If yes, then for which player?
b) What is the equilibrium for this game?
Q5. Consider the following strategic-form simultaneous game. Mark’s payoffs are listed first.
Mindy
X Y Z
A 80 , 30 0 , 20 20 , 20
Mark B 85 , 15 20 , 20 5, 5
C 95 , 25 5 , 25 5 , 25
a) Does either player have a dominant strategy? If yes, list it/them.
b) Does either player have a dominated strategy? If yes, list it/them.
c) List all pure strategy Nash equilibria of the above game
d) If Mindy’s payoffs in the top-left box (A,X) increased from 30 to 300, how would
your answer to part c above change? Explain.
e) Is there a Nash equilibrium if both players employ the Maximin strategy?
Q6. Ned and Ruth love to play “Hide and Seek." It is a simple game, that goes like this. Ruth
hides upstairs or downstairs. Ned can look upstairs or downstairs but not in both places. If he
finds Ruth, Ned gets one scoop of ice cream and Ruth gets none. If he does not find Ruth,
Ruth gets one scoop of ice cream and Ned gets none.
a) Draw the payoff matrix for this game.
b) Is there a dominant strategy for this game? If yes, then for which player?
c) What are the Nash equilibrium/equilibria for this game?
Q1. In Bakersville, there are two bakers, Andy and Cory. Andy's bread tastes just like Cory's;
nobody can tell the difference. Andy has constant marginal costs of $1 per loaf of bread. Cory
has constant marginal costs of $2 per loaf. Fixed costs are zero for both. The inverse demand
function for bread in Bakersville is
p(q)=6 −0.01q
,
where q is the total number of loaves sold per day.
a) Find Andy's Cournot reaction function.
b) Find Cory’s Cournot reaction function
c) Find the Cournot equilibrium quantities.
d) Find the profit for each baker
Q2. The inverse market demand curve for bean sprouts is given by
P(Y) = 100 −2Y ,
and the total cost function for any firm in the industry is given by TC(y)=4y.
a) If the bean-sprout industry were perfectly competitive, what would be the industry output
and the industry price?
b) Suppose that two Cournot firms operated in the market. What would be the reaction function
for each firm?
c) What would be the Cournot equilibrium in the above case?
d) What happens when the two firms decide to collude? What is the industry output and price
in event of collusion?
Q3. In a duopoly, the demand equations for both firms are as given:
q1=90-2p1+p2,
q2=90-2p2+p1
There are no variable costs associated with this industry (only a simplifying assumption; hard
to find in real life).
, a) What is the market equilibrium if the firms compete on the price front?
b) What is the market equilibrium if the firms compete in quantities?
c) Should they compete on prices or quantities?
Q4. Ann and Victoria are roommates. Each of them prefers a clean room to a dirty room, but
neither likes to clean the room. If both clean the room, they each get a utility of 5. If one
cleans and the other doesn't clean the room, the person who does the cleaning has a utility of
0, and the person who doesn't clean the room has a utility of 8. If neither cleans the room, the
room stays a mess and each has a utility of 1.
a) Is there a dominant strategy? If yes, then for which player?
b) What is the equilibrium for this game?
Q5. Consider the following strategic-form simultaneous game. Mark’s payoffs are listed first.
Mindy
X Y Z
A 80 , 30 0 , 20 20 , 20
Mark B 85 , 15 20 , 20 5, 5
C 95 , 25 5 , 25 5 , 25
a) Does either player have a dominant strategy? If yes, list it/them.
b) Does either player have a dominated strategy? If yes, list it/them.
c) List all pure strategy Nash equilibria of the above game
d) If Mindy’s payoffs in the top-left box (A,X) increased from 30 to 300, how would
your answer to part c above change? Explain.
e) Is there a Nash equilibrium if both players employ the Maximin strategy?
Q6. Ned and Ruth love to play “Hide and Seek." It is a simple game, that goes like this. Ruth
hides upstairs or downstairs. Ned can look upstairs or downstairs but not in both places. If he
finds Ruth, Ned gets one scoop of ice cream and Ruth gets none. If he does not find Ruth,
Ruth gets one scoop of ice cream and Ned gets none.
a) Draw the payoff matrix for this game.
b) Is there a dominant strategy for this game? If yes, then for which player?
c) What are the Nash equilibrium/equilibria for this game?
