| | Probability Payoffs Problem |
| | Taco Bell and Taco John's are two competing fast-food restaurant chains which serve Mexican inspired food at low prices. Many restaurants have holiday inspired menu items such as the Nachos Navidad at Taco John's.
Suppose two restaurants similar to Taco Bell and Taco Johns are considering the addition of a holiday menu item. Restaurant 1 is considering a holiday inspired burrito while Restaurant 2 is considering a holiday inspired quesadilla. If neither company releases either product, Restaurant 1 will earn their typical $10 million in quarterly profits while Restaurant 2 will earn $9 million. If Restaurant 1 decides to release their burrito, they will spend an additional $3 million introducing the new product but gain $4 million in additional revenue while Restaurant 2's revenue will be lower by $1 million. If Restaurant 2 decides to release their quesadilla, they will spend $3 million introducing the new product but gain $4 million in revenue while Restaurant 1's revenue will be lower by $1 million. If both firms release a holiday product, they will each spend $3 million but will only gain $1 million in revenue each. All relevant values are gathered in the table below.
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| | | | | Millions of Dollars |
| | | Typical sales, Restaurant 1 | | 10 |
| | | Typical sales, Restaurant 2 | | 9 |
| | | Only one holiday product is introduced: |
| | | Spendings on new product | | 3 |
| | | Additional revenue from new product | | 4 |
| | | Loss due to new product of the competitor | | 1 |
| | | Two holiday products are introduced: |
| | | Spendings on new product | | 3 |
| | | Additional revenue from new product | | 1 |
| | a) | Using the above information, create a payoff matrix using the template provided. Enter profits in millions of dollars. |
| | | | | Restaurant 2 (2) Quesadilla |
| | | | | Release | | Do Not Release |
| | | Restaurant 1 (1) Burrito | Release | 1 | | 1 |
| | | | | 2 | | 2 |
| | | | Do Not Release | 1 | | 1 |
| | | | | 2 | | 2 |
| | b) | If Restuarant 1 decides to release their burrito, what will Restaurant 2 decide to do? |
| | | | | Restaurant 2 will decide |
| | c) | If Restuarant 1 decides not to release their burrito, what will Restaurant 2 decide to do? |
| | | | | Restaurant 2 will decide |
| | Suppose Restaurant 1 and Restaurant 2 make this decision each year around the holidays. Restaurant 1 is a little more innovative and likes releasing limited time products; they tend to release a holiday menu item 75% of the time. Restaurant 2, on the other hand, is more conservative and only releases holiday menu items 40% of the time. Using this additional information and the profits calculated in the payoff table, answer the following questions.
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| | d) | What is the expected profit for each firm under each decision? Enter answers in millions of dollars, use the reference cells indicated for probabilities. |
| | | | | Probability of releasing holiday menu items by Restaurant 1 |
| | | | | Probability of releasing holiday menu items by Restaurant 2 |
| | | | | | Release | Do Not Release |
| | | | | Expected profit for Restaurant 1 |
| | | | | Expected profit for Restaurant 2 |
bahlman2
Bahlman_Chapter_8_Probability_Payoffs_Problem_Start.xlsx
