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This assignment is an easy 3 questions, I just need to see ALL the work. Game theory questions 

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Homework 5
Managerial Economics
Due Thursday, November 10, 2016
Instructions: Show all of your work!!!!
1.
Find all of the pure strategy Nash Equilibrium to the following simultaneous move game.
Column
A
B
C
D
E
a
7,7
3,6
8,6
1,14
19,8
b
2,16
1,2
8,11
5,6
11,14
Row
c
5,0
4,11
11,1
6,8
14,3
d
8,5
8,6
4,3
3,5
5,4
e
3,3
3,7
12,1
1,8
11,9
2.
Consider 2 firms selling fertilizer competing as Cournot duopolists. The inverse demand function
facing the fertilizer market is
? = ? −
±
?
²
, where
² = °
³
+ °
´
. For simplicity, assume that the
long-run marginal cost for each firm is equal to 1.
a)
Find the Cournot Nash equilibrium where the firms choose output simultaneously.
b)
Suppose the firms could collude, form a cartel, and split monopoly profits. How much would
each firm produce? What are there profits and how do they compare to part (a)?
c)
Will the cartel be sustained? In other words, will both parties maintain the outputs in (b)? Why
or why not? Explain.

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3.
Consider the following game where a potential market Entrant is trying to decide whether or not
to enter the market. The Incumbent firm is established and can choose to cut the price, maintain
the price, or raise the price of the god in hopes of deterring the Entrant from entering. The
payouts are given in the matrix below.
Cut Price
Maintain
Price
Raise
Price
Enter
-4,4
4,6
5,5
Stay Out
0,9
0,12
0, 13
a)
Suppose the Entrant and the Incumbent make their decisions simultaneously. Is there a pure
strategy Nash equilibrium? If so, what is it?
b)
Suppose the players move sequentially, and that the Entrant moves first. First set up the game
tree. What will be the subgame perfect Nash equilibrium outcome? Can the Incumbent deter
entry? Explain intuitively why or why not.
c)
Now suppose that the Incumbent moves first. Again, set up the game tree. What is the subgame
perfect Nash equilibrium outcome now? Can the Incumbent deter entry now?