2. Sequential Games
• Firms rarely engage in strategic
behavior once and then maintain course
• Firms respond to each other in a
sequential manner
• Ex: American introduces changes to basic
economy, United responds
• First mover is an early entrant and gains
dominant position, competition follows
• This is now a dynamic game, with firms
able to respond to each others’ moves
3. Stackelberg Model
• Similar to Cournout except firms
choose quantities sequentially
• One firm moves first and sets its
quantity, then the 2nd firm moves
• Firms trade goods on the market once
• Market clears at end of strategic action
• Setup:
• Market demand: P=A-BQ
• Firm 1 is leader. Firm 2 is follower
• Cost of production is c
• Industry output Q=!" + !$
4. Solving the Model
• Firm 1 acts first and chooses !"
• 1) Firm 1 estimates Firm 2’s response function
• Firm 2 sets MR=MC
• Since P=(A-B!")-B!# TR=P*!# $%#=(A-B!")-2B!#
• MR=MC: (A-B!")-2B!#=c !# =
('())
#+
-
,-
#
• 2) Firm 1 finds demand function by plugging in response function
• P = (A-B!#) - B!"àP = A -
(.(/)
#0
-
1-
#
− B!"àP=
'4)
#
−
+,-
#
5. Model Continued
• 3) Firm 1 forms profit function and solves for !"
• #" = (
&'(
)
−
+,-
)
− .)!"=(
&0(
)
−
+
)
!")!"
•
12-
1,-
=
&0(
)
-3!" = 0 !"=
&0(
)+
• 4) Firm 2 selects !) based on Firm 1’s selection of !"
• Firm 2 response function is !) =
(&0()
)+
-
,-
)
• !) =
(&0()
)+
-
&0(
4+
!)=
&0(
4+