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?