Discuss the differences among decision making under certainty, under risk and under complete uncertainty. (b) Bikram Shrestha is considering investing some money that he inherited. The following...

1)
a) In the environment of decision making under certainty, decision makers know for sure (i.e.,
with certainty) the payoff for every decision alternative. Typically, this means that there is only
one outcome for each alternative. In decision making under uncertainty, decision makers have
no information at all about the various outcomes. That is, they do not know the likelihood (or
probability) that a specific outcome will occur. In decision making under risk, decision makers
have some knowledge regarding the probability of occurrence of each outcome. The probability
could be a precise measure or an estimate. Regardless of how the probabilities are determined,
in decision making under risk, decision makers attempt to identify the alternative that
optimizes their expected payoff.
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 $20,000 - $20,000
= $50,000 = 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 market
conditions.
Therefore the expected profit is computed as:
P(a1) = (80,000)*P(S1) + (-40,000)P(S2) = 80,000*0.5 - 40,000*0.5 = 20,000
Similarly now for the small shop, the expected profit is computed as:
P(a2) = (30,000)*P(S1) + (-10,000)P(S2) = 30,000*0.5 - 10,000*0.5 = 10,000
Therefore Jerry should open the large shop.
b) Now for 3,000 in this case is a fixed cost, whether or not the large shop is opened or the smaller
one.
We already know that P(good market) = P( bad market) = 0.5
Also as 80% of the time he would correctly provide a favourable market prediction when the
market is good, therefore P(friend says good |...