Stackelberg Model

Question 1

What is the Stackelberg model?

Answer 1

Sequential Quantity Setting

Quantity Leadership.

Question 2

How do followers and leaders determine quantity?

Answer 2

Leaders must forecast what they believe the follower will set their quantity as, substitute that into their best response function. They must consider the follower’s maximisation problem.

Question 3

Sequential game strategy: Normal form game

Answer 3

Player one (leader) has two possible actions, whereas player two (follower) has 2 possible actions but four strategies.

Question 4

How do we solve for NE?

Answer 4

Both firms have to be best responding, even though there is a leader and a follower. We look down the game tree and look at what the follower is doing.

Question 5

How do we determine the profit maximising quantity for both firms?

Answer 5

We solve for follower’s strategy and find its best response function. The leader uses this to calculate its net or residual demand.

To find residual demand, we take the inverse demand function (like in Cournot), and rearrange to find the quantity the leader will sell.

Plug in followers best response function into firm A’s demand function.

Then find leader’s total revenue, derive, then put equal to MC.

Question 6

Difference between Cournot and Stackelberg Models

Answer 6

Cournot is simultaneous, Stackelberg is sequential.

Total output is greater in Stackelberg than Cournot.

Price is greater in Cournot than in Stackelberg.

Question 7

Profit differences between Cournot and Stackelberg Models.

Answer 7

Leader profit is greater under Stackelberg than Cournot.

Follower profit is greater under Cournot than Stackelberg.