Consider a Stackelberg duopoly: There are two firms in an industry with demand Q = 1 − Pd. The “leader” chooses a quantity qL to produce. The “follower” observes qL and chooses a quantity qF. Suppose now that the cost function is Ci(qi) = qi2 for i = L, F. (a) Find the subgame perfect equilibrium. (b) Compare the equilibrium you found with the Nash
Consider a Stackelberg duopoly: There are two firms in an industry with demand Q = 1 − Pd. The “leader” chooses a quantity qL to produce. The “follower” observes qL and chooses a quantity qF. Suppose now that the cost function is Ci(qi) = qi2 for i = L, F. (a) Find the subgame perfect equilibrium. (b) Compare the equilibrium you found with the Nash
Chapter8: Game Theory
Section: Chapter Questions
Problem 8.4P
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Consider a Stackelberg duopoly:
There are two firms in an industry with demand Q = 1 − Pd.
The “leader” chooses a quantity qL to produce. The “follower” observes qL and chooses a quantity qF.
Suppose now that the cost function is Ci(qi) = qi2 for i = L, F.
(a) Find the subgame perfect equilibrium.
(b) Compare the equilibrium you found with the Nash equilibrium if the game was simultaneous (i.e., Cournot competition). Is the Nash equilibrium of the Cournot game also a Nash equilibrium of the sequential game? Why or why not?
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