**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

allowed space.

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 |

Don’t Enter |

Don’t Invest |

Rival |

Enter |

X, 40 |

Don’t 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 | Probability | Return | Probability |

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?

____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________