1. The Oakland Bombers professional basketball team just missed making the playoffs last season and believes it needs to sign only one very good free agent to make the palyoffs next season. The team is considering four players: Barry Byr4d, Raneal O' Neil, Marving Johnson, and Michael Gordan. Each player differs accordign to position, ability, and attractiveness to fans. The payoffs (in $1,000,000s)to the team for each player, based on teh contract, profits from attendnace, and team product sales for serveral different season outcomes, are provided in teh following table.
Probability
Player Loser Competitive Makes Playoff
Byrd $-3.2 $1.3 4.4
O'neil -5.1 1.8 6.3
Johnson -2.7 0.7 5.8
Gordan -6.3 -1.6 9.6
Determine the best decision, using the followign decision criteria.
a. Maximax
b. Maximin
c. Hurwicz (alpha = 0.6)
d. Equal likelihood
2. In problem 14, the Bombers' management has determined the following probabilities of the occurrence of each future season outcome for each player:
Probability
Player Loser Competitive Makes Playoff
Byrd .15 .55 .30
O'neil .18 .26 .56
Johnson .21 .32 .47
Gordan .30 .25 .45
Compute the expected value for each player and indicate which player the team should try to sign.