We return to the prehistoric toy problem, but answer additional questions. As a reminder, here is the problem from "Prehistoric Transformer Toys.docx":

"MacMillan Toy Company has developed a collection of robot action figure toys that kids can transform into "prehistoric" insects with claws, fangs, and scorpion-like tails. MacMillan believes that its design is innovative enough that it can capture sales in this year's toy market before competitors can copy the major features and bring competing products to market. Nevertheless, MacMillan has some doubts about how appealing its design will be. Little market research has been done, so the market could be very enthusiastic or it could be indifferent.

As MacMillan's Marketing Manager, you must choose your launch strategy. A conservative strategy would be to launch a single type of the toy and see how it fares. This option would keep the costs down in case the market response is unenthusiastic. The bold strategy would be to launch the entire collection. This option would be quite profitable if the market response is positive but unprofitable if the response is indifferent. Finally, the moderate strategy would be to launch two of the types of the toy.

Reviewing data from previous launches, McMillan classifies the market responses to new toys (or toy collections) into three categories: Good, Fair, and Poor. The following table summarizes the profitability (in thousands of dollars) of each launch strategy under each possible market response:

		Market Response
		Good	Fair	Poor
	Single Type	100	60	-10
Decisions	Two Types	200	50	-40
	Entire Collection	300	40	-100

As covered in class, the probability of a good market response is 20%, a fair market response is 50%, and a poor market response is 30%. However, now the market for our toys is two years, and the table above only shows your profit (loss) in year 1. While the market response stays consistent over the two years (e.g., if it is fair in year 1, it's fair in year 2), you must keep your same launch strategy (single type, one type, entire collection) for the two years. Moreover, your profit (loss) in the second year depends on whether a competitor chooses to enter your market in year 2.

If no competitor enters the market, then your profit (or loss) in year 2 is half of the year 1 profit (or loss). However, if the market is good or fair, a competitor may enter the market and your year 2 profit is one quarter of the year 1 profit. Furthermore, the probability of a competitor entering the market depends on the market response and your launch strategy.

• Good market:In general, the competitor is more likely to enter if the market is good to grab some the available profits from a big pie. But, the likelihood of entering depends on your strategy:
• 1 Type: Since you have only produced one type, the competitor feels emboldened to enter and does so with 70% probability.
• 2 Types:If you build 2 types, the competitor is slightly dissuaded and enters with 60% probability.
• Entire Collection: If you build the entire collection, there's not much room for the competitor to enter. So, the competitor only enters with 20% probability.

• Fair market:In general, the competitor is less likely to enter if the market is fair since the available profits to grab is less. But, the likelihood of entering depends on your strategy:
• 1 Type: If you produce one type, the competitor enters with 50% probability.
• 2 Types:If you build 2 types, the competitor enters with 40% probability.
• Entire Collection: If you build the entire collection, the competitor enters with 10% probability.

1. Consider your payoff as the sum of the year 1 and year 2 profits (or losses). What is the maximax strategy? Provide a table to justify your answer.
2. What is the maximin strategy? Provide a table to justify your answer.
3. What is the minimax regret strategy? Provide a table to justify your answer.
4. What is the maximum expected payoff strategy and what is the expected profit under this strategy? Justify your answer with a decision tree. You may use any program such as Powerpoint, Excel, OneNote, or Paint to represent your decision tree. You may even neatly draw it on paper, scan it, and attach it to the homework. The main thing is that it is understandable. Points will be deducted if it's not clear what's being represented.