Questions 1-6

Here, I ask you to consider the sale of protection plans for electronic products. Specifically, consider the sale of a protection plan for a new $1,000 phone. The plan will pay out the full price of the phone (i.e., $1,000) in the event that it is damaged within three years of the purchase.

Phone buyers have a good sense of the probability that they will damage the phone. For example, they know whether they are clumsy, careless, have kids or pets around the house, etc etc. Specifically, there are four types of buyers: those that have accident probabilities of 0, 0.1, 0.2, and 0.3, respectively. There are an equal number of buyers in the four groups.

Buyers value the peace-of-mind they get from the protection plan. In dollar terms, this peace- of-mind is worth $150 to a buyer, regardless of the buyer's accident probability. (Even a completely safe buyer with accident probability of 0 experiences this benefit.)

A buyer's valuation of the protection plan is a combination of the plan's expected payout and the peace-of-mind benefit. As examples: A buyer with an accident probability of 0.1 places a value of 0.11,000 + 150 = $250 on the plan. Similarly, a buyer with an accident probability of

0.3 places a value of 0.31,000 + 150 = $450 on the plan.

As usual, assume that if a buyer is indifferent between purchasing and not purchasing the plan then the buyer purchases it. For example: A buyer with an accident probability of 0.1 would purchase a plan priced at $250.

The protection plan seller doesn't know buyers' accident probabilities.

Question 1

If the protection plan seller charges $250 for the protection plan: Which types of buyers will purchase it?

Question 2

If the protection plan seller charges $250 for the protection plan: What fraction of phone buyers purchase the plan?

Question 3

If the protection plan seller charges $250 for the protection plan: What is the protection plan seller's expected payout to the buyer on each plan sold?

Question 4

If the protection plan seller charges $250 for the protection plan: What is the protection plan seller's expected profit, per-buyer of the phone?

(That is: You need to take into account your answers to both questions 2 and 3.)

Question 5

What price maximizes the protection plan seller's expected profits?

Question 6

If the protection plan seller charges the profit-maximizing price, what fraction of buyers purchase the plan?

Question 7

Recall the "21 flags" game for game theory. Consider "99 flags," i.e., a game with the same rules, but in which there are initially 99 flags. The main rule is each player can take up to 3 flags in each turn. How many flags should the player with the first move take?

Question 8

Which player should win "99 flags"?

Questions 9-11

You, a real-estate developer, own a piece of land in Nassau, Bahamas, next to an equal-sized piece of land owned by a competitor. Both of you have the choice between building a casino and a hotel.

Payoffs are as follows:

If you both build hotels, you each make $20 million. If you both build casinos, you each make $30 million.

If you one of you builds a hotel and one of you builds a casino, the hotel-developer makes $50 million and the casino-developer makes $200 million.

(All the above payoffs are NPVs that take into account both initial development costs and subsequent profits.)

Your competitor is quicker than you are, and develops his/her land first.

Draw the tree-form that represents the above game, and then answer the following:

Question 9

Does your competitor build a hotel or a casino?

Question 10

Do you build a hotel or a casino?

Question 11

What is your competitor's payoff (i.e., $20 million, $30 million, $50 million, or $200 million)?

Questions 12-14

Next, we re-analyze the scenario of Questions 9-11 with just one change: It is widely known that you are a terrible hotel-operator, and consequently your payoff from operating a hotel is

$30 million less than the previous values, i.e., -$10 million if your competitor builds a hotel and

$20 million if your competitor builds a casino. All other payoffs are unchanged.

Question 12

Does your competitor build a hotel or a casino?

Question 13

Do you build a hotel or a casino?

Question 14

What is your competitor's payoff (i.e., $20 million, $30 million, $50 million, or $200 million)?

Questions 15 and 16

A tech-firm employs a coder. Over the next year, the coder can either work hard, or shirk ("quiet quit"). The coder dislikes working hard, and other things equal would prefer to shirk.

The firm observes the coder's performance over the next year. If the firm sees that the coder worked hard then the firm retains the coder. If instead the firm sees that the coder shirked, the firm decides whether to retain or fire the coder.

Payoffs are as follows (as usual, all payoffs are present values):

If the coder works hard, then his/her payoff (monetary income net of the costs of working hard) is $100K. The firm's payoff (value of output from the coder net of compensation paid) is $150K.

If the coder shirks and is subsequently fired, then the coder's payoff is $75K, and the firm'spayoff is$25K.

If the coder shirks and is subsequently retained, the coder's payoff is $150K, and the firm'spayoff is$50K.

Draw the tree-form that represents the above game, and then answer the following:

Question 15

Does the coder work hard or shirk?

Question 16

What is the firm's payoff?

Questions 17 and 18

Next, we re-analyze the scenario of Questions 15 and 16 with just one change: The coder is worse, so that the firm's payoffs are now:

$70K if the coder works hard

-$15K if the coder shirks and is fired

-$30K if the coder shirks and is retained

(To interpret the negative values: Recall that the firm's payoff is the value of coder-output net of the coder's compensation.)

Question 17

Does the coder work hard or shirk?

Question 18

What is the firm's payoff?

Question 19

Would the firm prefer to employ the better coder described in Questions 15 and 16, or the worse coder described in Questions 17 and 18?