ECO380H1 Lecture Notes - Lecture 6: Sequential Game, Root Mean Square, Economic Equilibrium
ECO380: Tutorial Problem Set - For Wednesday, March 8th 2018
1. [Stackelberg] Two rms compete in Stackelberg competition. They face a demand given by P=
240 −2Q= 240 −2(q1+q2). Firm 1 moves rst, and has a constant marginal cost of MC1= 20. Firm
2 moves second, and has M C2= 4q2. Solve for equilibrium quantities, and the equilibrium price in
the market.
2. [Backwards Induction] Two rms play a one-shot sequential game. We will denote actions taken by F1
with capital letters, and by F2 with lower case letters. F1 moves rst, and chooses either A or B.
•If F1 chooses A: F2 chooses between a and b. If F2 chooses b, both rms get a payo of 0. If F2
chooses a, then F1 chooses between C and D. If F1 chooses C, then F1 gets a payo of 2 and F2
gets a payo of 6. If F1 instead chooses D, F1 gets a payo of 1, and F2 gets a payo of 8.
•If F1 chooses B: F2 chooses between c and d. If F2 chooses d, F1 earns a payo of 6 and F2 earns
a payo of 4. If F2 chooses c, then F1 chooses between E and F. If F1 chooses E, both rms earn
a payo of 1. If F1 chooses F, then F2 moves again and chooses between e and f. If F2 chooses
e, then F1 earns a payo of 2 and F2 earns 0. If F2 chooses f, then F1 earns 0 and F2 earns 2.
Represent this game in extensive form (as a game tree). Use backwards induction to predict the
equilibrium outcome of the game, and describe the equilibrium strategies of each rm. Keep in mind
that a strategy species the action the rm would take, conditional on reaching a given node where
they get to move.
3. [Sequential Dierentiated Product] There are two rms (A and B) that produce dierentiated products
and face the following situation:
•QA= 200 −2PA+PB
•QB= 160 −4PB+ 2PA
•Constant MC of 10 for both rms.
Firm A sets their price before Firm B (this is sequential, rather than simultaneous competition). Solve
for equilibrium strategies, and the resulting equilibrium prices.
4. [Sequential Spatial Competition] In the lecture slides, we made our initial spatial price competition
sequential. Verify that our equilibrium p∗
1=c+ 1.5t, and p∗
2=c+ 1.25t.
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