Industrial Organization Problem Set 5
Question # 00438731
Posted By:
Updated on: 12/08/2016 02:42 AM Due on: 12/08/2016
Industrial Organization
Problem Set #5, Due Thursday, Dec 8, 10pm, online at NYU Classes
No late sets, one single file only
once submitted a file cannot be recalled 1) In Centipede, a game first introduced in 1962, there are two players. Player 1 moves first,
player 2 moves second. After at most two moves, the game ends. The game begins with
$1 sitting on the table. Player 1 can either take the $1 or wait. If player 1 takes the $1,
the game ends and player 1 can keep the $1. If player 1 waits the $1 quadruples to $4.
Now it is player 2’s turn. Player 2 can either take the entire $4 or split it evenly with
player 1.
a) Draw the extensive form for the game of Centipede.
b) What is the equilibrium to this game? Can player 2’s strategy of splitting the money
ever be part of an equilibrium outcome to this game?
c) Now suppose that Centipede has three moves. Player 2 can now either wait or split the
$4 with player 1. If player 2 waits the money on the table quadruples again, now to $16,
and player 1 can either it all or split it with player 2. Draw the extensive form for the new
game and solve for the equilibrium outcome. 2) Dry Gulch has two water suppliers. One is Northern Springs whose water is crystal clear
but not carbonated. The other is Southern Pelligrino whose water is naturally carbonated
but also somewhat hard. The marketing department of each firm has worked out the
following profit matrix depending on the price per 2-gallon container charged by each firm.
Southern Pelligrino’s profits are shown as the first entry in each pair. Southern
Pelligrino’s
price 3
4
5
6 3
24,
24
25,
20,
36
12, Northern Spring’s price
4
5
30,
36,
25
20
32,
41,
30,
40,
41
40
24,
36, 6
42,
12
48,
50,
36
48, a)
What is the Nash Equilibrium if the two firms set prices simultaneously?
b) What is the Nash Equilibrium if Northern Springs must set its price first and stick with it, and
Southern Pelligrino is free to respond as best as it can.
c) Describe in your own words why choosing price first is a disadvantage for Northern Springs.
(Just one or two sentences.)
Problem Set #5, Due Thursday, Dec 8, 10pm, online at NYU Classes
No late sets, one single file only
once submitted a file cannot be recalled 1) In Centipede, a game first introduced in 1962, there are two players. Player 1 moves first,
player 2 moves second. After at most two moves, the game ends. The game begins with
$1 sitting on the table. Player 1 can either take the $1 or wait. If player 1 takes the $1,
the game ends and player 1 can keep the $1. If player 1 waits the $1 quadruples to $4.
Now it is player 2’s turn. Player 2 can either take the entire $4 or split it evenly with
player 1.
a) Draw the extensive form for the game of Centipede.
b) What is the equilibrium to this game? Can player 2’s strategy of splitting the money
ever be part of an equilibrium outcome to this game?
c) Now suppose that Centipede has three moves. Player 2 can now either wait or split the
$4 with player 1. If player 2 waits the money on the table quadruples again, now to $16,
and player 1 can either it all or split it with player 2. Draw the extensive form for the new
game and solve for the equilibrium outcome. 2) Dry Gulch has two water suppliers. One is Northern Springs whose water is crystal clear
but not carbonated. The other is Southern Pelligrino whose water is naturally carbonated
but also somewhat hard. The marketing department of each firm has worked out the
following profit matrix depending on the price per 2-gallon container charged by each firm.
Southern Pelligrino’s profits are shown as the first entry in each pair. Southern
Pelligrino’s
price 3
4
5
6 3
24,
24
25,
20,
36
12, Northern Spring’s price
4
5
30,
36,
25
20
32,
41,
30,
40,
41
40
24,
36, 6
42,
12
48,
50,
36
48, a)
What is the Nash Equilibrium if the two firms set prices simultaneously?
b) What is the Nash Equilibrium if Northern Springs must set its price first and stick with it, and
Southern Pelligrino is free to respond as best as it can.
c) Describe in your own words why choosing price first is a disadvantage for Northern Springs.
(Just one or two sentences.)
-
Rating:
/5
Solution: Industrial Organization Problem Set 5