1. Dynamic games and First and Second Movers (The Stackelberg Model)
ECON 4100: Industrial Organization
Lecture 11
Dynamic games and First and Second Movers
(The Stackelberg Model)

2. Oligopoly Models There are three dominant oligopoly models
Cournot
Bertrand
Stackelberg
Now we will consider the Stackelberg Model (due to Heinrich von Stackelberg, 1934, about a century after Cournot’s)

3. Stackelberg Interpret in terms of Cournot
Firms choose outputs sequentially
leader sets output first, and visibly (IBM, Boeing, the leader is some easily visible firm )
follower then sets output
The firm moving first has a leadership advantage or first-mover advantage
can anticipate the follower’s actions
can therefore manipulate the follower
For this to work the leader must be able to commit to its choice of output
Strategic commitment has value

4. Stackelberg Equilibrium: an example
Both firms have constant
marginal costs of $10, i.e., c = 10 for both firms
Assume that there are two firms with identical products
As in our earlier Cournot example, let demand be:
P = Q = (q1 + q2)
Total cost for for each firm is:
C(q1) = 10q1; C(q2) = 10q2
Firm 1 is the market leader and chooses q1
In doing so it can anticipate firm 2’s actions
So consider firm 2. Demand is:
P = ( q1) - 2q2
Marginal revenue therefore is:
MR2 = ( q1) - 4q2

5. Stackelberg equilibrium (cont.)
Equate marginal revenue
with marginal cost
This is firm 2’s
best response
function
Stackelberg equilibrium (cont.)
Solve this equation
for output q2
But firm 1 knows
what q2 is going
to be
MR2 = ( q1) - 4q2 q2
Firm 1 knows that
this is how firm 2
will react to firm 1’s
output choice
MR = ( q1) - 4q2 = 10 = c
We can calculate that 22.5 is actually
the monopoly output. This is an important result. The Stackelberg leader chooses the same output as a monopolist would. But firm 2 is not excluded from the market
q*2 = q1/2
So firm 1 can
anticipate firm 2’s
reaction
Demand for firm 1 is:
P = ( q2) - 2q1
22.5
P = ( q*2) - 2q1
Equate marginal revenue
with marginal cost
P = (100 - (45 - q1)) - 2q1 S
11.25
=> P = 55 - q1
Solve this equation
for output q1 R2
Marginal revenue for firm 1 is: q1
MR1 = q1
22.5 45
55 - 2q1 = 10
=> q*1 = 22.5
=> q*2 = 11.25

6. Stackelberg equilibrium (cont.)
Leadership benefits
the leader firm 1 but
harms the follower
firm 2
Aggregate output is 33.75
Leadership benefits
consumers but
reduces aggregate
profits q2
Firm 1’s best response
function is “like”
firm 2’s
So the equilibrium price is $32.50 45
Firm 1’s profit is ( )22.5 R1
Compare this with
the Cournot
equilibrium
 p1 = $506.25
Firm 2’s profit is ( )11.25
 p2 = $
22.5
We can check that the Cournot equilibrium is: C 15 S
11.25
qC1 = qC2 = 15 R2 q1
The Cournot price is $40 15
22.5 45
Profit to each firm is $450

7. Stackelberg and Commitment
It is crucial that the leader can commit to its output choice
without such commitment firm 2 should ignore any stated intent by firm 1 to produce 45 units
the only equilibrium would be the Cournot equilibrium
In fact the model is incomplete unless we manage to explain this ability to make a credible commitment
It is not easy to commit in a credible manner to producing output

8. Stackelberg and Commitment
So how to commit?
prior reputation
investment in additional capacity
place the stated output on the market
Therefore, commitment could be better understood in terms of committing to the capability of producing output
We want to locked-in the cost of capacity (a sunk cost) to show that we mean business. This investment needs to be visible for it to be worthwhile

9. Stackelberg and timing
Finally, the timing of decisions matters (for some reason, one firm got there first and then has a way to commit through sunk investments in capacity)
There is much more we can learn later in terms of entry-deterrence too

10. Stackelberg and Efficiency
If unit costs are constant, Stackelberg’s equilibrium will result in a Pareto improvement relative to Cournot’s equilibrium, because the quantity produced increases
However, if the leader is relatively inefficient, then we cannot really say if this equilibrium will be better than the simultaneous choice of output
Passing output production from the efficient follower to the inefficient leader imposes an inefficiency that might not be counteracted by the efficiency increase associated with extra overall output
…and Stackelberg leaders can get very inefficient in real life (due to X-inefficiency for example)

11. Next: Monopoly Power and Predatory Conduct We will learn about:
Entry and exit, predatory conduct, and incumbent/entrant firm models
Dynamic strategic interaction and credible commitment
Limit pricing and public policy