Question

A television network is trying to decide during the summer which of the following three football games to televise on the Saturday following Thanksgiving Day: Alabama versus Auburn, Georgia versus Georgia Tech, or Army versus Navy. The estimated viewer ratings for the games depend on the win–loss records of the six teams, as shown in the following payoff table:

	Number of Viewers (1,000,000s)
	One Team Has
	Both Teams       Winning Record; One      Both Teams
	Have Winning      Team Has Losing          Have Losing
Game	Records                     Record                       Records
Alabama vs. Auburn	11.3	8.0	5.1
Georgia vs. Georgia Tech	10.0	9.3	5.3
Army vs. Navy	10.1	8.6	5.6

Determine the best game to televise and the payoff associated with it by using the following decision criteria.

a. Maximax

b. Maximin

c. Equal likelihood

d. Minimax regret

Answer 1

a.

Maximax - Maximizes the maximum payoff.

Maximum payoff for Alabama vs. Auburn game is 11.3

Maximum payoff for Georgia vs. Georgia Tech game is 10.0

Maximum payoff for Army vs. Navy game is 10.1

Maximum of maximum payoff is for Alabama vs. Auburn game. So, the best game to televise is Alabama vs. Auburn.

b.

Maximin - Maximizes the minimum payoff.

Minimum payoff for Alabama vs. Auburn game is 5.1

Minimum payoff for Georgia vs. Georgia Tech game is 5.3

Minimum payoff for Army vs. Navy game is 5.6

Maximum of minimum payoff is for Army vs. Navy game. So, the best game to televise is Army vs. Navy.

c.

Equal likelihood - Maximizes the average payoff.

Average payoff for Alabama vs. Auburn game is (11.3 + 8.0 + 5.1)/3 = 8.133333

Average payoff for Georgia vs. Georgia Tech game is (10.0 + 9.3 + 5.3)/3 = 8.2

Average payoff for Army vs. Navy game is (10.1 + 8.6 + 5.6)/3 = 8.1

Maximum of average payoff is for Georgia vs. Georgia game. So, the best game to televise is Georgia vs. Georgia.

d.

Minimax regret -

Regret = Best Payoff - Payoff Received

Regret table is,

Game	Records	Records	Records
Alabama vs. Auburn	11.3 - 11.3 = 0	9.3 - 8.0 = 1.3	5.6 - 5.1 = 0.5
Georgia vs. Georgia Tech	11.3 - 10.0 = 1.3	9.3 - 9.3 = 0	5.6 - 5.3 = 0.3
Army vs. Navy	11.3 - 10.1 = 1.2	9.3 - 8.6 = 0.7	5.6 - 5.6 = 0

Maximum regret of Alabama vs. Auburn game is 1.3

Maximum regret of Georgia vs. Georgia Tech game is 1.3

Maximum regret of Army vs. Navy game is 1.2

Minimum of all Maximum regret is for Army vs. Navy  game. So, the best game to televise is Army vs. Navy.