Chapter 26
Oligopoly,
mainly Duopoly
 Quantity
or price competitions.
Identical products:
p = p (Y ), Y = y1 + y2 .
Sequential games.
Backward solution.

Quantity leadership:
– Stackelberg model.
MR2 = p (y1+y2) + y2 dp / dy2 = MC2
gives the follower’s
reaction function
y2 = f 2 (y1) ;
then
max y1 p (y1+ f2 (y1 )) y1 – c1 ( y1 )
determines y1.
Example:
p ( y1 + y2) = a – b ( y1 + y2) ,
c = 0.
Price leadership:
The leader is supposed to set p first,
then max y2 py2 – c2 (y2)
gives
S2(p).
Now, the leader goes as a monopolist
facing the residual demand
R(p) = D(p) - S2(p).
Example:
D(p) = a – bp,
c2 ( y2 ) = y22 / 2,
c1 ( y1 ) = c y1.
Simultaneous
games.
Bertrand price competition
leads to p = MC even only
two firms.
Thus only quantity setting
consideration.
Cournot
model of quantity
competition:
max yi p( yi + yje) yi – ci ( yi ),
where yje is the output of Firm
j expected by Firm i,
gives yi = fi (yje),
then the consistence determines
the equilibrium.
Adjustment
to an equilibrium.
Several firms in Cournot equilibrium:
Y = y1 + … + y n ,
p (Y) [1 – si / |ε(Y)| ] = MCi(yi)
where si = yi / Y.