1. Chapter 26 Oligopoly, mainly Duopoly

2. Quantity or price competitions. Sequential games. Backward solution. Identical products: p = p (Y ), Y = y 1 + y 2.

3. Quantity leadership: – Stackelberg model.

4. gives the follower ’ s reaction function y 2 = f 2 (y 1 ) ; then max y 1 p (y 1 + f 2 (y 1 )) y 1 – c 1 ( y 1 ) determines y 1. dp / dy 2 = MC 2 MR 2 = p (y 1 +y 2 ) + y 2

5. Example: p ( y 1 + y 2 ) = a – b ( y 1 + y 2 ), c = 0.

6. The leader is supposed to set p first, then max Price leadership: y2 py 2 – c 2 (y 2 ) S 2 (p). gives R(p) = D(p) - S 2 (p). Now, the leader goes as a monopolist facing the residual demand

7. Example: D(p) = a – bp, c 2 ( y 2 ) = y 2 2 / 2, c 1 ( y 1 ) = c y 1.

8. Simultaneous games. Bertrand price competition leads to p = MC even only two firms. Thus only quantity setting consideration.

9. Cournot model of quantity competition: max yi p( y i + y j e ) y i – c i ( y i ), where y j e is the output of Firm j expected by Firm i, gives y i = f i (y j e ), then the consistence determines the equilibrium.

10. Adjustment to an equilibrium. where s i = y i / Y. p (Y) [1 – s i / |ε(Y)| ] = MC i (y i ) Y = y 1 + … + y n, Several firms in Cournot equilibrium: