Answer To: Discuss the differences among decision making under certainty, under risk and under complete...
David answered on Jan 02 2022
1)
a) Taking Decisions Under Certainty
If the outcomes are known and the values of the outcomes are certain, the task of the
decision maker is to compute the optimal alternative or outcome with some optimization
criterion in mind.
As an example: if the optimization criterion is least cost and you are considering two
different brands of a product, which appear to be equal in value to you, one costing 20% less
than the other, then, all other things being equal, you will choose the less expensive brand.
However, decision making under certainty is rare because all other things are rarely equal.
Linear programming is one of the techniques for finding an optimal solution under certainty.
Linear programming problems normally need computations with the help of a computer.
Taking Decisions Under Risk
The making of decisions under risk, when only the probabilities of various outcomes are
known, is similar to certainty.
Instead of optimizing the outcomes, the general rule is to optimize the expected outcome.
As an example: if you are faced with a choice between two actions one offering a 1%
probability of a gain of $10000 and the other a 50% probability of a gain of $400, you as a
rational decision maker will choose the second alternative because it has the higher
expected value of $200 as against $100 from the first alternative.
Taking Decisions Under Uncertainty
Decisions under uncertainty (outcomes known but not the probabilities) must be handled
differently because, without probabilities, the optimization criteria cannot be applied.
Some estimated probabilities are assigned to the outcomes and the decision making is done
as if it is decision making under risk.
b)
1) Optimist follows Maximax approach - Best of the Best.
Best of 3 alternatives are - Share market-$80,000, Bonds- 30,000, Real estate-25,000
Best of these best is Share market-$80,000
So the optimist chooses Share market decision.
2) Pessimist follows Maximin approach - Best of the Worst.
Worst of 3 alternatives are - Share market-$20,000, Bonds- 20,000, Real estate-15,000
Best of these worst is Share market or Bonds - $20,000
So the optimist chooses Share market or Bonds decision.
3) Regret = Best Payoff - Payoff received
Below is the regret table for the given payoff table.
Good Economy Bad Economy
Share
market
$80,000 - $80,000
= 0
$20,000 -$20,000
=0
Bonds
$80,000 - $30,000
= $50,000
$20,000 - $20,000
= 0
Real Estate
$80,000 - $25,000
= $55,000
$20,000 - $15,000
= $5,000
Maximum regret for Share market = $0
Maximum regret for Bonds = $50,000
Maximum regret for Real Estate = $55,000
The minimum of these 3 is Share market = $20,000.
So, criterion of regret alternative is Share market.
4) Probability of a good economy = 0.3
Probability of a bad economy = 1 - 0.3 = 0.7
Expected monetary value of Share Market = 0.3 * $80,000 + 0.7 * $20,000 = $38,000
Expected monetary value of Bonds = 0.3 * $30,000 + 0.7 * $20,000 = $23,000
Expected monetary value of Real Estate = 0.3 * $25,000 + 0.7 * $15,000 = $18,000
Maximum among these three is payoff of Share Market.
So, using expected monetary values, the optimum action is to choose Share Market.
5) Expected value without perfect information = Maximum expected monetary value = $38,000
Expected value with perfect information = 0.3 * Maximum of all payoff in good economy + 0.7 *
Maximum of all payoff in bad economy = 0.3 * $80,000 + 0.7 * $20,000 = $38,000
Expected value of perfect information = Expected value with perfect information - Expected
value without perfect information = $38,000 - $38,000 = $0
2)
a) We will find the expected profit for each of the scenarios - opening a large shop and opening a
small shop.
Expected profit in case a large shop is opened is computed as:
P(a1) = (80,000)*P(S1) + (-40,000)P(S2) where S 1 is the good condition and S2 is the poor...