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Ag Bus 452
Problem Set 2
260 Points
Due: 12/5/16
Dr. Hurley
Directions: Please answer all items on this problem set. You must show all your work.
1. Solve question U5 on page 209. (30 Points)
2. Solve question U6 on pages 209 and 210. (40 Points)
3. Solve question U11 on pages 211 and 212. (50 Points)
4. Find the best response functions for each player in the game below assuming that
retailer A plays AMGB with probability P and Retailer B plays AFGC with
probability Q. (10 points)
Retailer
A
Advertise Meat Gift
Baskets (AMGB)
Advertise Snack Gift
Baskets (ASGB)
Advertise Food Gift
Cards (AFGC)
(41,19)
(2,95)
Retailer B
Advertise Restaurant Gift
Cards (ARGC)
(26,37)
(52,89)
5. Draw each players best response function from question 4. (10 points)
6. Find all pure and mixed strategy Nash equilibrium(s) in the game below. What is the
expected payoff of the mixed Nash equilibrium for each player? (10 points)
7. Suppose that Retailer A decides to add a third strategy known as Advertise Wine Gift
Baskets (AWGB). If Retailer A plays this strategy and Retailer B plays AFGC, then
Retailer A will get a payoff of 50, while Retailer B will get a payoff of 5. If on the
other hand, Retailer A plays AWGB and Retailer B plays ARGC, the Retailer A will
get a payoff of 10 and player B will get a payoff of 10. Using a diagram, explain
what strategy Retailer A should choose in relationship to Retailer B choosing to play
AFGC with probability Q and ARGC with probability 1-Q. Hint: look on page 235.
(20 points)
8. Suppose you have the following game. Find all pure and mixed strategy Nash
equilibrium(s) in the game below. Assume Processor A plays Small with probability
P1, Medium with probability P2, and Large with probability 1 – P1 – P2 when he
plays his mixed strategy. Also assume Processor B plays Raise Price with probability
Q1, Keep Prices Constant with probability Q2, and Lower Prices with probability 1 –
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Last revised: 10/9/16
Q1 – Q2 when he plays his mixed strategy. What is the expected payoff for each
player when each player is playing the individual’s best mixed strategy? Does each
player prefer the pure strategy or mixed strategy? Please explain. (30 Points)
Processor A
Small
Medium
Large
Raise Price
(9,12)
(2,17)
(6,14)
Processor B
Keep Prices Constant Lower Prices
(17,2)
(10,9)
(9,15)
(14,16)
(9,17)
(12,15)
9. Suppose you are trying to hire for an entry level position in your agribusiness firm
where spreadsheet skills are an important component to the success of the candidate.
You have been authorized by your boss to pay an individual with superior skills
$60,000 and a person with good skills $40,000. Since the Agribusiness program at
Cal Poly has many courses that teach spreadsheet skills, you are inclined to recruit
from only this program.
Having talked to several professors, you have discovered that Cal Poly Agribusiness
students can be categorized as either having superior spreadsheet skills or good
spreadsheet skills. One way to measure an individual’s skills is by summing up the
person’s total quality points earned in the spreadsheet oriented classes where quality
points are defined as GPA in a class times the number of units in the class, e.g., if a
student gets an A in the class and the class is a 4 unit class, then the student is
awarded 16 quality points in total. Having talked to local tutors, you have found that
a student with good spreadsheet skills pays $500 per quality point while students with
superior spreadsheet skills pays $200 per quality point. Using the idea of an incentive
compatibility constraint, how many quality points would you need to request the
candidate to demonstrate on his/her transcript for the $60,000 job to ensure that you
get a superior spreadsheet skills candidate? (10 Points)
10. Solve problem S2 on pages 406 and 407. (50 points)
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Last revised: 10/9/16