Question

1. John Connor and his friends are planning a recreational outing and have constructed the following payoff table to help them decide which activity to engage in. Assume that the payoffs represent their level of death and dismemberment for each activity under the various possibilities for sentient cybernetic organisms they may encounter. They have no idea which of the terminators, the T-X, the T-1000, or the T-100, they might encounter on their outing.

Picnic		Rappelling		Disable Skynet
T-X	100		150		75
T-1000	150		125		100
T-100	200		50		125

1. If the group is optimistic, what decision should they make? [5 Marks]
2. If the group is conservative, what decision will they make? [5 Marks]
3. If the group chooses to minimize their maximum regret, what activity will they choose? [5 Marks]
4. If the probabilities of the T-X, T-1000, and T-100 are 0.2, 0.4, and 0.4, respectively, then what decision should be made using the expected value criterion? [5 Marks]

Answer 1

Activity / State of nature	TX	T1000	T100
Picnic	100	150	200
Rappelling	150	125	50
Disabling skynet	75	100	125

Note : Since higher value is undesirable, it has been written in negative

A. Optimistic Maximax decision making = Max [ Maximum output under each option]

= Max [ -200,-150,-125]=-125

which corresponds to Disabling skynet

B Conservative Maximin approach + Max [ Minimum output under each option]

= Max [ -100.-50.-75] = -50

which corresponds to Rappelling

C.

Regret table

Activity / State of nature	TX	T1000	T100
Picnic	25	50	150
Rappelling	75	25	0
Disabling skynet	0	0	75

Minimax regret = Min [ Max regret]

= Min [ 150,75,75] =75

which corresponds to Rappeling and disabling skynet, both have same output and thus equally favorable.

D ALl values are negative thus least negative value is most optimal.

EMV for picnic = 0.2x-100+0.4x-150+0.4x-200 = -160

EMV for Rappelling=  0.2x-150+0.4x-125+0.4x-50 =-100

EMV for Disabing skymet = 0.2x-75+0.4x-100+0.4x-125 =-105

The choice is Rappelling as it has highest EMV