Commerce 295/FRE 295
Fall 2014
Assignment 2
Assigned: Nov. 10/11
Due: Nov. 24/27
Instructions:
1. This assignment is due (in hardcopy form) by the beginning of your class on the date shown above. Assignments up to 24 hours late will receive a 25% penalty. Assignments more than 24 hours late will not be accepted. Late assignments can be given to Helen Ho in HA 266 or to Ines Bilec in the Undergraduate office or can be given to your instructor.
2. Extensions are possible only for genuine emergencies. Permission for the extension must be in advance (i.e. at least 24 hours before the assignment is due) and must be accompanied by appropriate documentation. See Ines Belic in the Undergraduate Office.
3. Show your working for all questions. Please be concise with your answers, and clearly identify the answer to the specific question you are being asked. Please carry 2 non-zero digits to the right of the decimal for answers that do not work out to whole numbers. Explain your reasoning where asked to do so.
4. Please use the remaining pages (not this page) as a template.You may type in your answers before printing out the document or you may print out the document and print your answers neatly by hand. Your answers must be neat and easily readable. If not, marks will be deducted or the answer will be ignored entirely. If in doubt, type your answer. Please confine your answer to the allowed space. Do question 7 before printing out the template as question 7 requires you to cut and paste a spreadsheet into the template.
5. Some of the questions have lines on which you are to write the answer. Do not exceed this space. Part of your task is to choose the right thing to say in a small space.
6. If you do not follow these instructions you will not get full credit for your work.
7. Students often like to work together in doing assignments. However, this is NOT a group assignment. It is primarily an individual effort. The basic rule about joint work is that it is acceptable to discuss questions with classmates but you must do the actual write-up of the assignment on your own. You must not copy someone else’s answer. Copied or plagiarized answers will be subject to appropriate penalties.
8. You may use pen or pencil but if you use pencil we cannot review situations where you think there is a marking mistake (except addition errors).
9. The assignment is challenging. Do not leave it to the last minute. When doing each question it is a good idea to find and read the relevant sections of the textbook first. Good Luck.
DATE: ______________
UBC Sauder School of Business
Commerce 295 / FRE 295
Fall 2014
Assignment 2
NAME: _______________________________________
STUDENT NUMBER:_______________________________________
SECTION NUMBER: _______________________________________
PROFESSOR: _______________________________________
MARKS: Points
1 /10
2 /10
3 _______ /10
4 /10
5 /10
6 /10
7 _ /10
8 _______ /10
9 /10
10 /10
TOTAL _________ / 100
Each question is worth 10 pts. Each part of each question is worth 5 pts. Show your working.
1. (Game Theory I)Suppose Air Canada and West Jet are deciding whether to offer a frequent flyer program (FFP). The annual profits of the two firms from each combination of strategies they choose is given in the following payoff matrix. The firms choose simultaneously.
Air Can.
West Jet
FFP
NO FFP
FFP
180, 150
200, 75
NO FFP
160, 210
225, 200
a)Identify any dominant strategies. Determine the Nash equilibrium in this game.(State the strategies and the payoffs.) Determine the maximin solution. Is this an example of a Prisoner’s Dilemma? In answering this question provide the relevant definitions and explain briefly how they apply.
b) Here is an entry game.
Firm 2
Firm 1
Do Not Enter
Enter
Do Not Enter
0,0
0,2
Enter
2,0
-1,-1
Identity any Nash equilibria in pure strategies. If firm 1 plays a mixed strategy of entering with 90% probability, what is the best response of firm 2? Is this combination of strategies a Nash equilibrium? Explain briefly. (Hint: when considering whether a proposed solution is a Nash equilibrium ask whether either firm regrets its choice whether its best response is different from what it actually chose.)
2. (Coordination Games). Consider the following network scheduling payoff matrix for Shaw Cable and Telus.
Shaw
Telus
Wednesday
Thursday
Wednesday
2, 2
10, 10
Thursday
12, 12
2, 2
a) Identify any Nash equilibria in this game. Explain briefly.
b)Would pre-play communication or application of the Pareto criterion be helpful in this game? Explain briefly.
3. (Repeated Games)Apple and Microsoft must decide on a pricing strategy for their tablet devices, the iPad and the Surface. Their respective marketing departments have determined two potential prices, one high and one low. The payoffs (in millions of dollars) are summarized in the table below.
Microsoft Surface
Low Price
High Price
Low Price
25, 20
60, 15
High Price
20, 50
55, 45
Apple iPad
a) What is the Nash equilibrium in the one-shot (static) game? Now suppose that the companies repeat this game every year with new versions of the tablets. Describe two different Nash equilibria of this infinitely repeated game and explain why each is an equilibrium. Your description of each equilibrium should be a pair of strategies (one for each firm), and the equilibrium payoffs for each firm per round.
b) A start-up competitor has developed a new technology that will make current tablet computers obsolete. There is no uncertainty about the success of the new venture, but it will take an additional 3 years to manufacture the required components. The founder of the start-up makes a public announcement that the new device will go on sale in three years. Do we expect Apple and Microsoft to make the most of the next three years by colluding on high prices? Explain your answer using appropriate terminology.
4. (Stackelberg Oligopoly)Consider the competition between Honda and Toyota in the compact car market. Each firm must commit to a production level at the beginning of the year. The payoffs for three possible outputs of each firm (in millions of dollars) are given in the table below. Suppose Honda preempts Toyota by finishing plans on its latest upgrade early, and therefore makes a public commitment on quantity before Toyota.
Toyota Corolla
High Quantity
Medium Quantity
Low Quantity
High Quantity
10, 10
30, 20
50, 25
Medium Quantity
20, 30
40, 40
60, 30
Low Quantity
25, 50
30, 60
50, 50
Honda Civic
a) Draw the relevant extensive form representation (game tree) for this strategic interaction. What is the sub-game perfect Nash Equilibrium?
b) Suppose Honda must spend an additional 15 million dollars to be in the position to announce first, and otherwise the two firms announce simultaneously. Is it profitable for Honda to expedite planning? Now suppose that Toyota goes first unless Honda spends the $15 million to expedite planning, in which case Honda goes first. Would the 15 million dollar investment be worthwhile in this case? Explain.
5. Sequential Games
a) Consider the following game tree describing strategic interaction between an incumbent monopolist and a potential rival.
100, 0
Dont Enter
Dont Invest
Rival
Enter
X, 40
Dont Enter
80, 0
Incumbent
Invest
Rival
10, Y
Enter
For what range of values of X and Y will the incumbent deter entry by investing? Show your working.
b) A mining company is considering starting operations in a foreign country known to be rich in mineral deposits but with an unreliable government. Extracting the minerals will be very profitable, but requires extensive and costly digging before anything can be extracted from the ground. Explain briefly using appropriate terminology why the company might be hesitant to start work on this potentially profitable project. (No diagram is needed.)
__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
6. Behavioral Economics
a. Consider a game with 10 players. Each person submits an integer between 0 and 100. The winner of the game is the person who submits a number closest to 60% of the average number submitted. The winner gets a prize of $1000 and no one else gets anything. If two or more people tie for the win they share the prize equally. Assuming that all players are fully rational and that rationality is common knowledge, what is the Nash equilibrium? If you were playing this game with randomly chosen first year UBC students, would you bid the Nash equilibrium value?
The Nash equilibrium is __________________________________________________________.
We know this is a Nash equilibrium because _____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
If I were trying to win this game I would submit the value _________________________.
I think this offers the best chance of success because _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.
b. State whether prospect theory, the reciprocity norm, or neither can explain the following phenomena. Circle the correct response and explain briefly.
Framing effects. Prospect Theory or Reciprocity Norm or Neither. ______________________________________________________________________________________________________________________________________________________________
The Certainty Effect. Prospect Theory or Reciprocity Norm or Neither.
______________________________________________________________________________________________________________________________________________________________
Overconfidence.Prospect Theory or Reciprocity Norm or Neither.
______________________________________________________________________________________________________________________________________________________________
Behavior in Ultimatum Games. Prospect Theory or Reciprocity Norm or Neither.
______________________________________________________________________________________________________________________________________________________________
Bounded Rationality. Prospect Theory or Reciprocity Norm or Neither.
______________________________________________________________________________________________________________________________________________________________
7. (Uncertainty)A manager must choose one of four advertising strategies, with the following characteristics. The manager cares only about the expected value and variance of the projects.
Strategy
Return with Bad Luck
Probability of Bad Luck
Return with Good Luck
Probability of Good Luck
A
2
0.7
12
0.3
B
4
0.6
9
0.4
C
1
0.2
6
0.8
D
2
0.5
12
0.5
a. Put this data into a spreadsheet, add three columns with headings EV, VAR, and SD, and use the spreadsheet to calculate the expected value, variance, and standard deviation. Paste the resulting spreadsheet in the space below.
Which strategy would be chosen by a risk preferring manager? a risk neutral manager? a risk averse manager?
A risk preferring manager would choose _____ because _________________________________ ______________________________________________________________________________________________________________________________________________________________
A risk neutral manager would choose ________ because _________________________________ ______________________________________________________________________________________________________________________________________________________________
For a risk averse manager we can say ________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________
b. Suppose utility is given by U = ?Y where Y is the return. For Strategy B what is the expected utility and what is the risk premium? Draw the associated diagram showing the risk premium. (Do not worry about making the diagram precise. Just illustrate the general idea, but include the relevant numbers on the axes.)
8. (Adverse Selection)Consider the used car example described in Q&A 15.1, except the numbers are different. Buyers value lemons at $5000 and good used cars at $10,000. The reservation price of lemon owners is $4000 and the reservation price of owners of good used cars is $7,500. Owners know the quality of the cars but buyers do not. (Show your working.)
a. Suppose that 40% of the used cars are good used cars and 60% are lemons. Describe the equilibrium.
b. Now suppose that 60% of the cars are good used cars and 40% are lemons. Describe the equilibrium now.
9. (Agency) Priscilla hires Arnie to manage her business; both of them are risk neutral. The following table shows Priscilla’s profits (before paying Arnie) for two different levels of Arnie’s effort and two different market situations. If Arnie provides low effort, his cost of effort is zero but if he provides high effort his cost is 10. Weak demand and strong demand are equally likely. (Show your working.)
Weak Demand Strong Demand
Low Effort 20 40
High Effort 40 80
a) If Priscilla offers a profit sharing contract in which Arnie gets 30% of the profits, what effort level would Arnie provide? Calculate Priscilla’s expected net profits (after paying to Arnie) under this contract.
b) If Priscilla offers a bonus contract in which Arnie gets a base salary of 4 (no matter whether demand is weak or strong) plus 80% of all profits exceeding 40, what effort level would Arnie choose now? Which contract (profit sharing or bonus) would Priscilla prefer? Which contract would Arnie prefer?
10. (Economic Research)
Holloway, Lee and Shen (2014) study the determinants of cross-border leveraged buyouts.
a) The authors present a stylized model of the global competition among buyout firms.
i) What factors in the model determine the number of acquisitions by buyout firm in each country?
ii) Can you think of any other factors that likely play a role in the real world?
iii) Where do these other factors implicitly enter the equation for the number of completed buyout deals by each investor in each country?
b) The authors test the predictions of the model using a sample of worldwide buyout deals.
i) Which two countries dominate as home countries for buyout firms in the sample?
ii) How do the authors test the prediction that transaction costs associated with remote ownership impact the number of deals? How do they measure the theoretical cost mitigation ability?
______________________________________________________________________________________________________________________________________________________________
_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
iii) Are results consistent with the predictions of the model? How can you tell?
____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________