Ag Bus 452
Problem Set 1
200 Points
Due: 10/26/16
Dr. Hurley
Directions: Please answer all items on this problem set. You must show all your work.
1. Given the game tree below, write out the set of strategies for each player. The Aijk
represents the action that player i can take at the jth node for the kth possible action at
the jth node. The payoffs are written where player 1’s payoff is listed first and player
2’s payoff is listed second. The payoff represent a ranking of outcomes where lower
numbers are considered better, i.e., 1 is considered the best. (10 Points)
Player 1
Player 2
A221
3,2
A151 2 , 7
Player 1
A152
A222
A111
7,4
A231
6,6
S112
A113
4,8
A232
22
A241
1,1
22
A161
A242
22
5,7
A162
8,5
2. For the game in question 1, what is the rollback equilibrium? Please briefly explain.
(10 Points)
3. Suppose there are two players, Annie and Buck. Annie and Buck’s sinister friend
puts 10 one-dollar bills on the floor. He gives each the opportunity to take either 1 or
2 dollars from the pile, one person after the other in succession. He tells then that the
person who picks up the last dollar on the floor gets to take all the money the other
Page 1 of 3
Last revised: 10/9/16
person has picked up, as well as, keep the money in his or her own hand. If the
sinister friend chose Annie to go first, who would obtain all the money in the end?
Please explain. (Hint: you may want to think of the game from the end.) (20 Points)
4. In the game discussed in question 3, does any player have an advantage? Please
explain. (10 Points)
5. Given the game tree below, write out the set of strategies for each player. The Aijk
represents the action that player i can take at the jth node for the kth possible action at
the jth node. The payoffs are written where player 1’s payoff is listed first, player 2’s
payoff is listed second, and player 3’s payoff is written third. The payoff represent a
ranking of outcomes where highest numbers are considered better, i.e., 8 is
considered the best. (10 Points)
Player 3
Player 2
A221
3,2,6
A351
Player 1
A352
A222
A111
2,7,8
7,4,2
A231
6,6,7
S112
A113
4,8,5
A232
22
A241
1,1,3
22
A361
A242
22
5 , 7, 4
A362
8,5,1
6. For the game in question 5, what is the rollback equilibrium? Please briefly explain.
(10 Points)
Page 2 of 3
Last revised: 10/9/16
7. Suppose you have the following game. Please provide the best response for each
player given the other person’s strategy. You should have six best responses. (10
Points)
Processor A
Small
Medium
Large
Raise Price
(68,77)
(50,24)
(48,93)
Processor B
Keep Prices Constant Lower Prices
(82,86)
(55,16)
(98,84)
(69,60)
(34,27)
(62,8)
8. In the game provided in question 7, are there any dominant or dominated strategies?
Please briefly explain. (10 Points)
9. In the game provided in question 7, is the game dominance solvable? Please briefly
explain. (10 Points)
10. What is/are the Nash Equilibrium in question 7? Please explain (10 Points)
11. Solve question U10 on page 131. (30 Points)
12. For question 11, write out each person’s best response function to the others’
strategies. (10 Points)
13. Suppose you have two campus food trucks at Cal Poly vying to sell you each’s
signature item. The first truck, known as Gutter Dining, sells a bratwurst sandwich
that is very popular. The second truck, known as Juicelicious, sells a frothy vegetable
and apple juice concoction that has just won a campus newspaper award for best
drink on campus. Suppose you can represent the quantity sold of bratwurst as
QB = 38 – 1PB – 2PJ and the quantity sold of juice as QJ = 28 – 2PJ – PB where PB is
the price of the bratwurst and PJ is the price of the juice. If the cost to produce one
bratwurst sandwich is $8 and the cost to produce one juice drink is $2, what is each
food truck’s profit function? (10 Points)
14. For question 13, what is the best response function for each food truck? Draw these
functions on a graph. (10 Points)
15. For questions 13 and 14, what is the equilibrium price that each truck will charge, the
equilibrium output that each produces, and the profit that each makes? (10 Points)
16. Solve question U8 parts a and b on page 173. (Answer may not come out clean.) (20
Points)
Page 3 of 3
Last revised: 10/9/16