I. Problem 1: 40%) Pizza King and Noble Greek are two competing restaurants. Eac
ID: 2921392 • Letter: I
Question
I. Problem 1: 40%) Pizza King and Noble Greek are two competing restaurants. Each must determine simultaneously whether to undertake small, medium or large advertising campaigns. Pizza King cannot predict or inluence the choice of their competitor, but they believe that it is equally likely that Noble Greek will undertake either of the campaigns. Given the actions chosen by each restaurant, Pizza King's profits are as shown in the table below. Pizza King chooses Small Medium Large Small $6,000 $5,000 $9,000 Noble Greek chooses Medium $5,000 $6,000 $6,000 Large $2,000 $1,000 $0 (a) [20%) For the Maximin and Expected Payoff criteria, determine Pizza King's choice of advertising campaign (b) [20%] If Pizza King could pay a Noble Greek's ennployee to learn Noble Greek's plans, what is the maximum amount of money they would be willing to pay for the insider's tips?Explanation / Answer
(a) FOr Maximin Criteria,
Under this criteria we will see that what maximum bad can happen in each case.So, here we will see case by case:
(a) FOr small pizza sizes :Minimum payoff = $ 2000
for medium pizza sizes : Minimum payoff = $ 1000
for large pizza sizes : Minimum payoff = $0
so wewill say Small pizza sizes, Pizza king has maximum minimum payoff so the company will choose this.
Expected payoff critere:
Here probability of Noble Greek choosing any type of pizza size = 1/3
so,
Expected Payoff for Small pizza size = 1/3 * ( 6000 + 5000 + 2000) = $ 4333.33
Expected payoff for Medium pizza size = 1/3 * (5000 + 6000 + 1000) = $ 4000
Expected payoff for Large pizza size = 1/3 * (9000 + 6000 + 0) = $ 5000
so, we will choose largepizza size
(b) Here we have to find that the maimum payoff we can achieve :
so now we will now the plan of Noble Greek what it is making.
so maximum payoff = 1/3 * 9000 (when small pizza is made by NG)) + 1/3 * 6000 * (when medium pizza is made by NG) +1/3 * 2000 ( when large pizza is made by NG)
= $ 5666.67
so maximum amount of money for insider tips to be paid = $ 5666.67 - $ 5000 = $ 666.67