Decision making under uncertainty
• Laplace criterion or criterion of rationality or
Bayes’ criterion
• Here there is no information about the states
of nature.
• All states of nature are considered equally
likely
• the probability of all states of nature is
considered equal
Bayes’ criterion
• For example if there are 3 states of nature
Demand = High;
Demand = Medium;
Demand = Low
• These are three states of nature therefore
probability of occurrence of each = 1/3
• Suppose there are 4 states of nature then
probability of each will be 1/4
Bayes’ criterion
States of nature (Estimated level of sales)
Alternatives 15000 10000 5000 Expected payoff
P = 1/3 P = 1/3 P = 1/3
Egg shampoo 30 10 10 30*1/3 + 10*1/3 +
10*1/3 = 50/3
Clinic shampoo 40 15 5 40*1/3 + 15*1/3 +
5*1/3 = 60/3
Deluxe 55 20 3 55*1/3 + 20*1/3 +
shampoo 3*1/3 = 80/3
solve
Alternatives
States of nature Stockpile A1 Do not Stock Pile A2
Strike S1 60000 20000
No Strike S2 40000 30000
Maximax criterion
Alternatives
States of nature Stockpile A1 Do not Stock Pile A2
Strike S1 60000 20000
No Strike S2 40000 30000
Maximax 60000 30000
Maximin
Alternatives
States of nature Stockpile A1 Do not Stock Pile A2
Strike S1 60000 20000
No Strike S2 40000 30000
Maximin 40000 20000
Minimax Regret Criterion
Alternatives
States of nature Stockpile A1 Do not Stock Pile A2
Strike S1 0 40000
No Strike S2 0 10000
Minimax regret 0 40000
Hurwicz criterion with α = 0.6
Alternatives
States of nature Stockpile A1 Do not Stock Pile A2
Strike S1 60000 20000
No Strike S2 40000 30000
P = α *max + (1-α P =60000*.6 + 40000*.4 P =20000*.6 + 30000*.4
)* min P = 52000 P = 24000
Bayes’ criterion
Alternatives
States of nature Stockpile A1 Do not Stock Pile A2
Strike S1 60000 20000
No Strike S2 40000 30000
P = α *max + (1-α P =60000*1/2+ P =20000*1/2+ 30000*1/2
)* min 40000*1/2 P = 25000
P = 50000
