Question

A television network is attempting to decide during the summer which of the following three football games to televise on the Saturday following Thanksgiving Day: Alabama vs. Auburn, Georgia vs. Georgia Tech, Miami vs. Virginia Tech. The estimated viewer ratings (millions of homes) for the games depend on the win-loss records of the six teams, as shown in the following payoff table. Determine the best game (most viewers) to televise using the following decision criteria.

		States of Nature - Number of viewers
		One team has
	Both Teams	Winning record	Both teams
	Have winning	One team has	Have losing
Games	Records	Losing record	Records
Alabama vs. Auburn	10.3	7.3	5.4
Georgia vs. Georgia Tech	9.6	8.1	4.8
Miami vs. Viriginia Tech	12.5	6.5	3.2

Determine the best decision using the following decision criteria. Calculate and show values for each alternative (except for #7). Assume that the probability of both teams having a winning record is 20%, and both teams having a losing record is 25%.

            1. Maximax

            2. Maximin

            3. Criterion of Realism (a = .4)

            4. Minimax

            5. Expected Value

            6. Expected Opportunity Loss

            7. Expected Value of Perfect Information

Answer 1

Solution

1) maximax :

maximum of each row = 10.3 , 9.6 , 12.5

maximum frothese = 12.5 so decision = Miami vs. Viriginia Tech

2) maximin :

minimum of each column = 5.4, 4.8 , 3.2

maximum from these = 5.4

decision : Alabama vs. Auburn

3) realism :

maximum value of each row * a + minimum value of eac row * (1-a)

= 10.3*0.4 + 5.4*0.6 , 9.6*0.4 + 4.8*0.6 , 12.5*0.4 + 3.2*0.6 = 7.36, 6.72, 6.92

DECISION = Alabama vs. Auburn

4) minimax

maximum of each row = 10.3 , 9.6 , 12.5

min = 9.6

decision = Georgia vs. Georgia Tech