Question

A payoff table is given as

	State of Nature
Decision	s1	s2	s3
d1	250	750	500
d2	300	- 250	1200
d3	500	500	600

a.	What choice should be made by the optimistic decision maker?
b.	What choice should be made by the conservative decision maker?
c.	What decision should be made under minimax regret?
d.	If the probabilities of d1, d2, and d3 are .2, .5, and .3, respectively, then what choice should be made under expected value?
e.	What is the EVPI?

Answer 1

a.

Optimistic choice - Use maximax rule. First, compute the maximum payoff for each alternative. Then select the alternative which gives the maximum of these maximums.

	State of Nature			Max
Decision	s1	s2	s3	Payoff
d1	250	750	500	750
d2	300	-250	1200	1200
d3	500	500	600	600

So, the best decision is d₂.

b.

Conservative choice -  Use maximin rule. First, compute the minimum payoff for each alternative. Then select the alternative which gives the maximum of these minimums.

	State of Nature			Min
Decision	s1	s2	s3	Payoff
d1	250	750	500	250
d2	300	-250	1200	-250
d3	500	500	600	500

So, the best decision is d₃.

c.

Minimax regret

First, develop the regret matric by subtracting each payoff from its corresponding column maxima.

Regret matrix	State of Nature
Decision	s1	s2	s3
d1	250	0	700
d2	200	1000	0
d3	0	250	600

Next, compute the maximum regrets for each alternative and select the alternative which gives the minimum of these maximum regrets.

Regret matrix	State of Nature			Max
Decision	s1	s2	s3	regrets
d1	250	0	700	700
d2	200	1000	0	1000
d3	0	250	600	600

So, the best decision is d₃.

d.

Compute the expected payoff and the alternative which gives the maximum expected payoff

	State of Nature			Expected
Decision	s1	s2	s3	Payoff
d1	250	750	500	575^^
d2	300	-250	1200	295
d3	500	500	600	530
Probability	0.2	0.5	0.3

^{^^} 250*0.2 + 750*0.5 + 500*0.3 = 575

So, the best decision is d₁.

e.

Expected value of perfect information, EVPI = Expected value with perfect information - max. EMV

= 0.2*Max(250,300,500) + 0.5*Max(750,-250,500) + 0.3*Max(500,1200,600) - 575

= 260