ECON 3600
Assignment 5
Due Thursday, March 7th.
Dynamic Games (Problems 1 and 2 adapted from Bierman and Fernandez. Problem 3 from Yale
Open Course.)
1. Solve the following threeplayer game using backwards induction:
Players are A, B, and C. Payoffs are written as (A's payoff, B's payoff, C's payoff)
Solution: (1,2,2) is the BI solution.
2. Stackelberg Competition
Two firms are competing over quantities.
There is no cost of production and the product is
exactly the same whether purchased from Firm 1 or Firm 2.
The market demand is:
Market Price = 10
–
(Q
1
+Q
2
)
a. Assume both firms choose their output quantities simultaneously. Find the Nash equilibrium
price and output. Show your work.
Firm 1's profit function is: (
10
–
(Q
1
+Q
2
))Q
1
.
FOC: 10  2Q
1
 Q
2
= 0
BR
1
(Q
2
) = (10  Q
2
)/2
C
B
A
(2, 1, 0)
(1, 2, 2)
(0, 100, 100)
(100, 100,1)
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View Full Documentsince the game is symmetric, setting Q
1
= Q
2
gives us:
Q
1
* = Q
2
*= 3.33. And P = 3.33.
b. Assume the game is sequential: Firm 1 chooses its output quantity first, then Firm 2 chooses
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 Spring '12
 daniel
 Economics, Equilibrium, Game Theory, Firm, Absentee landlord

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